
	Where results make sense

Topic: Dimension of an algebraic variety

Related Topics

Network Mapping

Shovel

Caturix

Baccio Bandinelli

East Randolph, New York

Worldwide Developers Conference

Alexandria, South Dakota

Boomerang Nebula

Berkeley

Pineville, Louisiana

The Bold and the Beautiful

Agastya

Biograph Theater

Adenosine monophosphate

In the News (Mon 7 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Dimension article - Dimension Latin degrees freedom measurements shape Physical dimensions - What-Means.com (Site not responding. Last check: 2007-09-18)
		Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space.
		Time is frequently referred to as the "fourth dimension"; time is not the fourth dimension of space, but rather of spacetime.
		The Krull dimension of a commutative ring, named after Wolfgang Krull (1899 - 1971), is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring.
	www.what-means.com /encyclopedia/Dimension (596 words)

	Dimension - Open Encyclopedia (Site not responding. Last check: 2007-09-18)
		It is somewhat different to the three spatial dimensions in that there is only one of it, and movement is only possible in one direction.
		In physics, the dimension of a quality is the expression of that quality in basic units: the dimension of speed, for example, is length divided by time.
		In the SI system, the dimension is given by the seven exponents of the fundamental quantities.
	open-encyclopedia.com /0d (636 words)

	Algebraic groups (Site not responding. Last check: 2007-09-18)
		For the purposes of algebraic geometry over the complex numbers, an abelian variety is a complex torus (a torus of real dimension 2n that is a complex manifold) that is also a projective algebraic variety of dimension n, i.e.
		An abelian function is a meromorphic function on an abelian variety, which may be regarded therefore as a periodic function of n complex variables, having 2n independent periods, equivalently, it is a function in the function field of an abelian variety.
		This theory was much later put on an axiomatic basis, in which abelian varieties are by definition the connected groups in the category of projective algebraic varieties.
	read-and-go.hopto.org /Algebraic-groups (436 words)

	Dimension : 2d (Site not responding. Last check: 2007-09-18)
		For any topological space, the Lebesgue covering dimension is defined to be n if any open cover has a refinement (a second cover where each element is a subset of an element in the first cover) such that no point is included in more than n+1 elements.
		The Krull dimension of a commutative ring is defined to be the maximal length of a strictly increasing chain of prime ideals in the ring.
		Demogorgon, is an instance of this--it fills the mind as the most the 'cars drawn by rainbow-winged steeds A wild-eyed charioteer urging their flight.
	www.freetemplate.ws /2d/2d.html (880 words)

	Glossary
		An algebraic map or regular map or morphism of quasiprojective varieties is a map of whose graph is closed.
		An algebraic group is a group G in the category of quasiprojective varieties i.e.
		A homogenous space is a variety X such that there is an algebraic group G and a transitive action on X for which GxX → X is a morphism.
	www.math.purdue.edu /~dvb/algeom2.html (786 words)

	DIMENSION FACTS AND INFORMATION
		It is somewhat different from the three spatial dimensions in that there is only one of it, and movement seems to be possible in only one direction.
		Theories such as string_theory predict that the space we live in has in fact many more dimensions (frequently 10, 11 or 26), but that the universe measured along these additional dimensions is subatomic in size.
		In the physical sciences and in engineering, the ''dimension'' of a physical quantity is the expression of the class of physical unit that such a quantity is measured against.
	www.palfacts.com /dimension (874 words)

	Glossary of terms for Fermat's Last Theorem
		An algebraic variety that has a group structure where the multiplication and inversion mappings are morphisms of algebraic varieties.
		A complete algebraic variety which is an algebraic curve that is essentially the quotient space of the upper half of the complex plane by the action of a subgroup of finite index of the modular group.
		An elliptic curve E for which there is a modular curve X of a certain kind and a surjective map X -> E. Such an elliptic curve is said to have a "parameterization by modular functions".
	gyral.blackshell.com /flt/flt10.htm (2633 words)

	Algebraic Geometry : A First Course (Graduate Texts in Mathematics) by Joe Harris [ISBN: 0387977163] - Find Cheap ...
		The first part is concerned with introducing basic varieties and constructions; it describes, for example, affine and projective varieties, regular and rational maps, and particular classes of varieties such as determinantal varieties and algebraic groups.
		In addition, algebraic groups on varieties are discussed in lecture 10, allowing one to discuss a kind of glueing operation on varieties, just as in geometric topology, namely by taking the quotient of varieties via finite groups.
		The author then moves on to giving a more rigorous formulation of dimension, giving several different definitions, all of these conforming to intuitive ideas on what the dimension of an algebraic variety should be, and also one compatible with a purely algebraic context.
	www.gettextbooks.com /isbn_0387977163.html (1548 words)

	Computing the Dimension of a Projective Variety: the Projective Noether Maple Package
		Using the algorithm of §3.1, we know that at step m of the iteration the dimension of the variety is at most m-1.
		When trying to certify the dimension, the a priori size of the matrices (and the DAG's) involved in the pure SLP strategy (BDE) prevents it from defeating rewriting techniques regularly, especially when they are implemented in an incremental way.
		In situations of low codimension, our implementation gives an upper bound for the dimension and, with an extremely low (uniform) probability of failure, certifies that this bound is sharp much more quickly than the implementation of Gröbner basis used.
	pauillac.inria.fr /algo/papers/html/GiHaLeMaSa97/GiHaLeMaSa97.html (4914 words)

	philosophy notes
		The replacement for the finite cardinality of the group is its dimension as an algebraic variety.
		An algebraic group is then an abstract algebraic variety with a binary and a unary operation which satisfy the axioms of groups and are morphisms of algebraic varieties.
		An algebraic group $G$ is a structure whose universe is some subset of $k^n/\iso$ and whose relations are all those definable in the field $k$.
	www.math.uic.edu /~jbaldwin/pub/phil.html (2052 words)

	[No title]
		An affine G-variety Y is called stable if points of Y in general position have closed G-orbits.
		For an algebraic group G, defined over an algebraically closed field of characteristic zero, there is a natural partial order on the set of G-actions on algebraic varieties: X >= Y if there exists a dominant G-equivariant rational map (i.e., a compression) from X to Y. Alternatively, one can consider regular, rather than rational, compressions.
		The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
	www.math.ubc.ca /~reichst/abstract.html (2805 words)

	geomsem05
		Schubert varieties are Gorenstein, analogous to Lakshmibai and
		These are real varieties X which have a nice cellular decomposition after base extension to the complex numbers.
		An exterior differential system (EDS) generated by n 2-forms for vanishing induced torsion and n n-1-forms for vanishing Ricci tensor is shown to be well posed by calculation of its Cartan characters (for n=4, and the right signature, this is vacuum relativity.) Calculation of these uses a Monte Carlo character program due to H. Wahlquist.
	www.math.tamu.edu /~jml/geomsem05.html (1113 words)

	DIMACS Workshop ...
		Here we present an extention of the Viro gluing theorem aimed at smoothing stronger singularities, which is a natural way to explore the classifications of real algebraic zeros.
		An overview of the algorithms for operations on Pfaffian and fewnomial functions and sets, their complexity, and unsolved problems will be presented.
		An unexpected application of this library is in automated proving of elementary geometry theorems.
	dimacs.rutgers.edu /Workshops/Algorithmic/abstracts.html (2693 words)

	[No title] (Site not responding. Last check: 2007-09-18)
		The homogeneous polynomials of degree 3 in 4 variables form a vector space of dimension 20, so the associated projective space is a P^{19}.
		The image B(P^3 x P^{9}) is an algebraic variety of dimension 12 and degree 220 (= {9+3\choose3}).
		If it did have 7 generators (so that the variety is what is known as a complete intersection), then they would have to have an average degree of more than 30.
	www.math.niu.edu /~rusin/known-math/98/cubic_surf (474 words)

	commalg.org - the center for commutative algebra
		Quasi-isomorphic differential graded algebras give rise to 2-isomorphic differential graded schemes and a differential graded algebra can be recovered up to quasi-isomorphism from the differential graded scheme it defines.
		For a large class of singular varieties $Y$, we show that $\D_Y$-modules are equivalent to stratifications on $Y$ and thus in particular are unaffected by a class of homeomorphisms, the {\em cuspidal quotients}.
		These varieties can be interpreted as generalized tangent bundles over the classical determinantal varieties; a special case of these varieties first appeared in a problem in commuting matrices.
	www.commalg.org /preprints/2002_12.shtml (2220 words)

	University of Arizona: Mathematical Software (Site not responding. Last check: 2007-09-18)
		Rychlik's research is in the area of dynamical systems; in particular, their algebraic aspects.
		An example would be an explicit computation of the dimension of an algebraic variety, as a function of parameters.
		One applet allows the user to specify a function of two dimensions to be plotted.
	uranium.math.arizona.edu /software.html (863 words)

	Hironaka (Site not responding. Last check: 2007-09-18)
		Two algebraic varieties are said to be equivalent if there is a one-to-one correspondence between them with both the map and its inverse regular.
		Two varieties U and V are said to be birationally equivalent if they contain open sets U' and V' that are in biregular correspondence.
		His work generalised that of Zariski who had proved the theorem concerning the resolution of singularities on an algebraic variety for dimension not exceeding 3.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Hironaka.html (290 words)

	Van_der_Waerden (Site not responding. Last check: 2007-09-18)
		As well as an almost unbelievable range of mathematical research interests, van der Waerden stimulated research in Zurich by supervising over 40 doctoral students during his years there.
		In algebraic geometry van der Waerden defined precisely the notions of dimension of an algebraic variety, a concept intuitively defined before.
		His work in algebraic geometry uses the ideal theory in polynomial rings created by Artin, Hilbert and Emmy Noether.
	www-history.mcs.st-and.ac.uk /history/Mathematicians/Van_der_Waerden.html (522 words)

	Citations: Proving by example and gap theorems - Hong (ResearchIndex) (Site not responding. Last check: 2007-09-18)
		An acclaimed approach in this area is due to Wu [21, 23, 22] who applied the concept of characteristic sets to geometric theorem proving.
		Carr a and Gallo [1] and Gallo [7] devised a method using the dimension underlying the algebraic variety.
		An acclaimed approach in this area is due to Wu [18, 20, 19] who applied the concept of characteristic sets to geometric theorem proving.
	citeseer.ist.psu.edu /context/147530/0 (1439 words)

	DIMENSION FACTS AND INFORMATION (Site not responding. Last check: 2007-09-18)
		Classical physics theories describe three physical dimensions: from a particular point in space, the basic directions in which we can move are up/down, left/right, and forward/backward.
		Movement in any other direction can be expressed in terms of just these three.
		It is different from the three spatial dimensions in that there is only one of it, and movement seems to be possible in only one direction.
	www.amysflowershop.com /dimension (872 words)

	Dimension : 3d (Site not responding. Last check: 2007-09-18)
		'Scott was the soul coming up from Kelso at sunset, and as there was to be a fine moon, I proposed to stay an hour.html">hour and enjoy it.
		"I never saw most familiar terms with the cicerone, pointed to an empty niche, and your niche.
		I'll send it to you." "How happy you have made that man," is constantly grudging it house-room.
	www.wordlookup.net /3d/3d.html (648 words)

	General algorithms
		Note that the algorithm is doubly exponential in dimension,
		It can theoretically be declared to be efficient on a space of motion planning problems of bounded dimension (although, it certainly is not efficient for motion planning in any practical sense).
		Since cylindrical algebraic decomposition is doubly exponential, it led many in the 1980s to wonder whether this upper bound can be lowered.
	msl.cs.uiuc.edu /planning/node318.html (378 words)

	Symbolic Computation, Polynomial Equations and Differential Algebra (Site not responding. Last check: 2007-09-18)
		CGBLisp is a software system for dealing with systems of algebraic equations with parameters.
		The most ambitious part of the differential algebra project is to merge the approach of Comprehensive Grobner Basis developed in CGBLisp with the Kuranishi-Cartan theory, and devise a software package which is capable of handling all cases of PDAE's.
		CGBlisp is an experimental Common Lisp package for calculating an object called Comprehensive Groebner Basis (the notion developed by V. Weispfenning).
	alamos.math.arizona.edu /~rychlik/symcomp.html (303 words)

	Computing Roadmaps of Semi-algebraic Sets on a Variety (Extended Abstract) (ResearchIndex) (Site not responding. Last check: 2007-09-18)
		We consider a semi-algebraic set S defined by s polynomials of degree at most d in k variables contained in an algebraic variety V of dimension k 0 defined as the zero set of a polynomial of degree d and two points defined...
		0.3: On the combinatorial and algebraic complexity of Quantifier..
		70 piano movers (context) - Schwartz, On Roy On the combinatorial and algebraic complexity of Quantif..
	citeseer.ist.psu.edu /91982.html (390 words)

	UC Berkeley Mathematics (Site not responding. Last check: 2007-09-18)
		Canonical map (that is the map induced by the canonical linear series) of an algebraic curve C of genus g > 1 is reasonably well understood: either it is an embedding or maps C 2:1 onto a rational normal curve.
		For an algebraic variety of dimension two or higher, the canonical map is much more subtle due to, among other things, the existence of higher degree covers.
		I will talk about some recent results (with F. Gallego) on the canonical map of a surface of general type and its connection to the so-called “mapping geography” of surfaces of general type.
	math.berkeley.edu /index.php?module=calendar&calendar[view]=event&id=674 (142 words)

	cohn2
		Andre' Galligo and Carlo Traverso: "Practical Determination of the dimension of an algebraic variety", in E. Kaltofen and S.M. Watt, Eds "Computers and Mathematics", pages 46-52, 1989.
		Cohn: "An explicit modular equation in two variables and Hilbert's Twelfth problem", Math.
		Cohn, J. Deutch: "An explit modular equation in two variables for Q[sqrt(3)]", Math.
	www.math.uic.edu /~jan/Demo/cohn2.html (53 words)

	Talk Abstract: Complexity and applications of parametric algorithms of computational algebraic geometry (Site not responding. Last check: 2007-09-18)
		Complexity and applications of parametric algorithms of computational algebraic geometry
		The Comprehensive Groebner Basis algorithm of V.~Weispfenning can be applied to compute the maximal dimension of an algebraic variety depending on parameters and a variety of other problems which can be solved in the non-parametric case with the help of Groebner bases.
		A variety of examples from several areas of mathematics and science will be presented, including bifurcation theory, mechanics and chemistry.
	www.ima.umn.edu /dynsys/wkshp_abstracts/rychlik1.html (107 words)

	[No title] (Site not responding. Last check: 2007-09-18)
		# Andre' Galligo and Carlo Traverso: # "Practical Determination of the dimension of an algebraic variety", # in E. Kaltofen and S.M. Watt, Eds "Computers and Mathematics", # pages 46-52, 1989.
		# H. Cohn: "An explicit modular equation in two variables and # Hilbert's Twelfth problem", Math.
		# H. Cohn, J. Deutch: "An explit modular equation in two variables # for Q[sqrt(3)]", Math.
	liawww.epfl.ch /Coconut-benchs/Polynomial/cohn2.mod (63 words)

	ProjectiveHilbertPolynomial (Site not responding. Last check: 2007-09-18)
		dim -- dimension of a projective Hilbert polynomial
		* -- multiply a projective Hilbert polynomial by an integer
		-- evaluate a projective Hilbert polynomial at an integer
	www.dmi.units.it /assistenza/Macaulay2-0.8/132.html (80 words)

Try your search on: Qwika (all wikis)