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	Projective plane - Wikipedia, the free encyclopedia
		In mathematics, a projective plane has two possible definitions, one of them coming from linear algebra, and another (which is more general) coming from the combinatorics of block designs.
		The most common projective plane is the real projective plane, which is a topological surface with surprising geometric properties; after that is the complex projective plane of algebraic geometry, a topological four-dimensional manifold.
		In the case of finite projective planes, the only proof known of the purely geometric statement that Desargues theorem then implies Pappus' theorem (the converse being always true and provable geometrically) is through this algebraic route, using Wedderburn's theorem that finite division rings must be commutative.
	en.wikipedia.org /wiki/Projective_plane (1038 words)

	Complex projective plane (Site not responding. Last check: 2007-10-22)
		The Betti numbers of the complex projective plane are
		The middle dimension 2 is accounted for by the homology class of the complex projective line, or Riemann sphere, lying in the plane.
		In birational geometry, a complex rational surface is any algebraic surface birationally equivalent to the complex projective plane.
	www.sciencedaily.com /encyclopedia/complex_projective_plane (273 words)

	Complex projective plane - Wikipedia, the free encyclopedia
		It is known that any non-singular rational variety is obtained from the plane by a sequence of blowing up transformations and their inverses ('blowing down') of curves, which must be of a very particular type.
		is obtained from the plane by blowing up two points to curves, and then blowing down the line through these two points; the inverse of this transformation can be seen by taking a point P on the quadric Q, blowing it up, and projecting onto a general plane in P
		The group of birational automorphisms of the complex projective plane is the Cremona group.
	en.wikipedia.org /wiki/Complex_projective_plane (236 words)

	Research/Spreads and Translation Planes
		A spread in a projective 3-space is a set of lines such that each point of the space is incident with exactly one line.
		Of special interest are examples of topological translation planes and their automorphism groups, where, for instance, classical line geometry is used in order to construct examples of spreads.
		The translation plane arising from this spread is the complex projective plane.
	www.geometrie.tuwien.ac.at /havlicek/proj304.html (703 words)

	first (Site not responding. Last check: 2007-10-22)
		The problem of computing the number N(d) of degreed rational curves through 3d-1 points in the complex projective plane has very classical geometric origins.
		MU's Jan Segert recently succeeded in constructing the quantum cohomology Frobenius manifold for the complex projective plane, completing a project that he started nearly two years ago.
		The construction is based on a classifying space for resonant isomonodromic deformations and combines techniques of differential geometry and algebraic geometry to obtain an explicit global description.
	www.math.missouri.edu /~news/issue4/first.html (404 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		CR singular immersions of complex projective spaces article abstract Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification.
		A classification theorem relates equivalence classes of projections to congruence classes of matrix pencils.
		Maps from the 2-sphere to the complex projective plane, which generalize stereographic projection, and immersions of the complex projective plane in four and five complex dimensions, are considered in detail.
	www.ipfw.edu /math/Coffman/projabs.txt (100 words)

	Salomon Bochner Lectures, 2004-2005 (Site not responding. Last check: 2007-10-22)
		This series of lectures will aim to provide an overview of a relatively recent set of techniques which can be used to study the topology of symplectic manifolds (a class of smooth manifolds which naturally generalizes the better understood case of smooth projective varieties and plays a central role in mathematical physics).
		This establishes a bridge between the topology of symplectic manifolds and that of singular plane curves.
		We will discuss in particular two concrete examples for which the conjecture can be checked explicitly: weighted projective planes, and Del Pezzo surfaces (blowups of the projective plane).
	math.rice.edu /Calendar/bochner06.html (468 words)

	LMS Proceedings Abstract, paper PLMS 1500 (Site not responding. Last check: 2007-10-22)
		Hamiltonian stationary tori in the complex projective plane
		In this paper we analyze these surfaces in the complex projective plane: in a previous work we showed that they correspond locally to solutions to an integrable system, formulated as a zero curvature on a (twisted) loop group.
		Here we give an alternative formulation, using non-twisted loop groups and, as an application, we show in detail why Hamiltonian stationary Lagrangian tori are finite type solutions, and eventually describe the simplest of them: the homogeneous ones.
	www.lms.ac.uk /publications/proceedings/abstracts/p1500a.html (130 words)

	projective plane - OneLook Dictionary Search
		Projective Plane : A Glossary of Mathematical Terms [home, info]
		Projective Plane : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include projective plane: finite projective plane, real projective plane, complex projective plane, projective plane dissecti, projective plane pk2
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=projective+plane (134 words)

	CR singular immersions of complex projective spaces - Coffman (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: Quadratically parametrized smooth maps from one complex projective space to another are constructed as projections of the Segre map of the complexification.
		Real congruence of complex matrix pencils and complex projections..
		Coffman, CR singular immersions of complex projective spaces, to appear in Beitrage zur Algebra und Geometrie.
	citeseer.ist.psu.edu /coffman02cr.html (519 words)

	Page Title (Site not responding. Last check: 2007-10-22)
		I then used this result to show that any invariant curve, for an AS self-map of a minimal rational surface, must either be rational or elliptic.
		In the second part of my thesis I studied quadratic birational self-maps of the complex projective plane that possess an invariant curve.
		Using these results on the complex projective plane, I calculated the topological entropy for some families of quadratic self-maps of the real projective plane.
	www.nd.edu /~djackso1/page6.html (147 words)

	Brunella: Foliations on the complex projective plane with many parabolic leaves
		Brunella: Foliations on the complex projective plane with many parabolic leaves
		Foliations on the complex projective plane with many parabolic leaves.
		GARNETT, Foliations, the ergodic theorem and brownian motion, Jour.
	www.numdam.org /item?id=AIF_1994__44_4_1237_0 (174 words)

	Equisingular Families Of Plane Curves With Many (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		Abstract: We present examples of equisingular families of complex projective plane curves with plural connected components that are not distinguished by the fundamental group of the complement.
		0.7: The Braid Monodromy Of Plane Algebraic Curves And Hyperplane..
		2 the fundamental group of the complement of certain plane cur..
	citeseer.ist.psu.edu /598974.html (317 words)

	1. Complex projective plane serves as a canvas
		But, as it is standard in quantum theory, proportional vectors describe the same state - the overall phase of the vector has no physical significance.
		Therefore, in geometrical terms, the set of all pure states is nothing but the projective complex space
		, can be also thought of as the projective light cone - the space of light directions.
	quantumfuture.net /quantum_future/papers/qfract/node18.html (189 words)

	/usr/local/etc/httpd/htdocs/archive/sem_coll_1999
		There is a close and useful analogy between the study of complex projective plane curves and the study of knots and links in the three dimensional sphere.
		In both areas, geometric information about the embedding can be gleaned from information about the homotopy type and fundamental group of the complement.
		For plane algebraic curves, a standard method for presenting the homotopy type of the complement uses the Zariski-van Kampen method of fibrations.
	www.math.buffalo.edu /archive/sem_coll_1999.html (4132 words)

	Find in a Library: Abelian coverings of the complex projective plane branched along configurations of real lines
		Find in a Library: Abelian coverings of the complex projective plane branched along configurations of real lines
		Abelian coverings of the complex projective plane branched along configurations of real lines
		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	worldcatlibraries.org /wcpa/ow/0ddeab0420e24a56a19afeb4da09e526.html (67 words)

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