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Topic: Zariski

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Oscar Zariski

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	OSCAR ZARISKI
		Zariski, an adopted member of the Italian school, reformulated the subject in in terms of modern algebra and provided the basis for its twentieth-century development.
		Zariski, as a Jewish socialist with Communist sympathies, was unwilling to become a citizen of Fascist Italy and so could not join the university faculty; he juggled odd jobs while Yole taught full-time.
		Ironically, it was during the writing of this book that Zariski became "disgusted" with the Italian methods and their lack of rigor, and started on his project of rebuilding algebraic geometry on the foundation of modern commutative algebra, particularly the work of Noether and Krull.
	www.usna.edu /Users/math/meh/zariski.html (943 words)

	PlanetMath: Zariski topology
		The Zariski topology is the predominant topology used in the study of algebraic geometry.
		Every regular morphism of varieties is continuous in the Zariski topology (but not every continuous map in the Zariski topology is a regular morphism).
		This is version 1 of Zariski topology, born on 2002-05-11.
	planetmath.org /encyclopedia/ZariskiTopology.html (150 words)

	Oscar Zariski - Wikipedia, the free encyclopedia
		Oscar Zariski (24 April 1899 - 4 July 1986) was a Belarusian-American mathematician, one of the most influential theorists of algebraic geometry in the 20th century.
		Zariski emigrated to the USA in 1927 supported by Solomon Lefschetz.
		The Zariski topology, as it was later known, is adequate for biregular geometry, where varieties are mapped by polynomial functions.
	en.wikipedia.org /wiki/Oscar_Zariski (632 words)

	Zariski (Site not responding. Last check: 2007-10-15)
		Zariski had gone to Italy to escape the problems in Belarus and the Ukraine.
		In 1981 Zariski was awarded the Steele Prize by the American Mathematical Society for the cumulative influence of his total mathematical research.
		All of Zariski's work has served as a basis for the present flowering of algebraic geometry and the current school uses his work and ideas in the modern development of the subject.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Zariski.htm (1513 words)

	[No title]
		Zariski's defence of electronic legal journals - and his opposition to electronic self-publication and the central collection or connection of legal scholarship in archives - appears to rest on six propositions, four of which are more or less "technical", and two of which are more broadly "theoretical".
		Zariski's purported distinction between active and passive scholarly formats is likely to become largely irrelevant with the development of "intelligent agent" technology which is still in its protean stages (although basic commercial versions are already on the market).
		Zariski suggests that science differs from law insofar as the former discipline is more tightly structured and hence generates scholarship that is more readily classifiable.
	www.law.pitt.edu /hibbitts/archie.htm (4204 words)

	Heller Ehrman - Daniel A. Zariski Bio (Site not responding. Last check: 2007-10-15)
		Zariski is a former judicial clerk to the Honorable Carolyn Dineen King, United States Fifth Circuit Court of Appeals.
		Zariski has represented companies in the consumer electronics, software, insurance and tobacco industries in defense of putative class actions brought against those companies under a variety of state and federal common law and statutory causes of action.
		Zariski serves as a faculty member for Heller Ehrman’s Deposition Training and Trial Advocacy Programs, and is a frequent luncheon speaker on deposition strategy, insurance litigation issues and tactics, discovery practice and complex case management.
	www.hewm.com /en/attorneys/bios/Zariski_Daniel.html (665 words)

	Zariski biography
		In Rome Zariski came under the influence of the great algebraic geometers Castelnuovo, Enriques and Severi.
		It was while Zariski was in Rome that Enriques suggested that Ascher Zaritsky, as he was then called, change his name to the Italian sounding Oscar Zariski.
		Both Zariski and Weil learnt much in discussions, often arguments, about the material that Zariski was presenting.
	www-history.mcs.st-andrews.ac.uk /Biographies/Zariski.html (1523 words)

	Resolution of Singularities
		Zariski's work was obviously a summit of mathematics in the 40's and will be analyzed forever by the coming mathematicians.
		With it Zariski showed easily that either all coefficients are isolated with respect to blow--ups, hence there is a reduction of the number of variables or there is a reduction of multiplicity $m$ which is certainly an improvement on the singularity.
		Secondly Zariski followed in his procedure the ``Person Algorithm'' which is a plain generalization of continuous fractions.
	www.math.purdue.edu /~ttm/resolution.html (805 words)

	Zariski topology - Wikipedia, the free encyclopedia
		In this sense, the Zariski topology is an organizational tool rather than an object of study (compare with the role of the topology in algebraic topology).
		In fact, the Zariski topology is the weakest topology (with the fewest open sets) in which this is true and in which points are closed.
		This is one instance of the geometric unsuitability of the Zariski topology.
	en.wikipedia.org /wiki/Zariski_topology (1421 words)

	Oscar Zariski Summary
		Oscar Zariski was one of the most influential mathematicians working in the field of algebraic geometry in the twentieth century.
		Zariski became professor at Harvard University in 1947, retiring in 1969.
		In 1945 he fruitfully discussed foundational matters for algebraic geometry with André Weil; Weil's interest was in putting an abstract variety theory in place, to support the use of the Jacobian variety in his proof of the Riemann hypothesis for curves over finite fields, a direction rather oblique to Zariski's interests.
	www.bookrags.com /Oscar_Zariski (685 words)

	Zariski Topology
		The zariski topology is consistent with the metric topology, though it is weaker.
		Let k be a field with a valuation metric, such as the p-adic numbers, or the fraction field of any pid, or the completion thereof.
		Since addition and multiplication are continuous, polynomials are continuous, and within this context the zariski topology is consistent with the metric topology, but weaker, as shown by the powers of p in k
	www.mathreference.com /ag,zar.html (549 words)

	INI : Abstracts : NCGW03 : Zariski Geometries: from classical to quantum (Site not responding. Last check: 2007-10-15)
		Zariski geometries are abstract topological structures with a dimension, satisfying certain assumptions.
		Algebraic varieties over algebraically closed fields and compact complex manifolds are Zariski geometries and for some time it was thought that all Zariski geometries are of this kind.
		Conversely, we show in particular that any quantum algebra at roots of unity of certain type coordinatises a geometric object which is a Zariski geometry.
	www.newton.cam.ac.uk /programmes/NCG/abstract3/zilber.htm (127 words)

	Zariski topology - QEDen
		Zariski topology is a variety of topology that looks at underlying properties of surfaces, ignoring many of their geometric properties.
		This page is a short definition of the term "Zariski topology".
		Ask any questions about "Zariski topology" by editing the talk page.
	www.qeden.com /wiki/Zariski_topology (71 words)

	[No title]
		The authors show that the Zariski topology associated to an algebraically closed field can be characterized, as a combinatorial geometry, by a handful of familiar and elementary properties.
		Theorem B. Any ample Zariski geometry is a finite cover of the canonical Zariski geometry on the projective line over some algebraically closed field.
		The proof amounts to a reversal of Cramer's paradox: given a curve $C$ of degree $d$, the number of points needed to determine an algebraic curve of much higher degree is more than the maximum number of points of intersection of this curve with $C$; so $C$ must be a component of some algebraic curve.
	www.cs.bgu.ac.il /~kojman/colloquium/zilberrev.html (1479 words)

	E-Journals, Archives and Knowledge Networks: A Commentary on Archie Zariski's Defense of Electronic Law Journals
		In his First Monday article "Never Ending, Still Beginning: A Defense of Electronic Law Journals from the Perspective of the E-Law Experience", Professor Archie Zariski asserted that, despite recent musings to the contrary, electronic legal periodicals have a bright future in the age of the Internet.
		In a wide variety of academic disciplines, including law, electronic journals are generally presumed to represent the leading edge of innovation in the presentation and delivery of scholarship.
		Professor Zariski describes one of E Law's authors - David Loundy - as having done precisely this.
	firstmonday.org /issues/issue2_7/hibbitts/index.html (4237 words)

	Proving Zariski Space Theorems in Isabelle: A Case Study in the Application of Automated Theorem Proving ...
		Fortunately, there has been a steady increase of the usability, capability and efficiency of automated theorem proving, and the time may now be ripe to re-evaluate the applicability of theorem proving technology to mathematical research.
		Zariski Spaces is a branch of algebra that is being actively developed.
		Zariski Spaces is the tip of a pyramid of mathematical theories: semi-groups, groups, rings, topology, etc. Many of these theories are already implemented in Isabelle but some will need to be added.
	www.inf.ed.ac.uk /teaching/courses/diss/props/031_bundy16.html (473 words)

	Automated Theory Formation for Tutoring Tasks in Pure Mathematics (Site not responding. Last check: 2007-10-15)
		For instance, Zariski Topologies and the study of varieties have played an important role in the development of Algebraic Geometry, and in particular, the Hilbert Nullstellensatz, which is one of the fundamental results in Algebraic Geometry.
		The study of semimodules in general has already yielded many applications to computer science [golan:monograph], and since Zariski Spaces are first and foremost semimodules, it is possible that their study will promote further advances in theoretical computer science.
		The proposed route to Zariski spaces is via: semigroups, semirings and semimodules, followed by groups, rings and modules and finally, using a cross domain approach, Zariski spaces.
	www.doc.ic.ac.uk /~sgc/html_papers/colton_radm02.html (5755 words)

	Apocrypha
		Once, while Zariski was lecturing in a seminar, Grothendieck kept asking him why he didn't prove his result for all schemes, not just varieties, but Zariski simply responded that it didn't work.
		When Grothendieck realized he was wrong, Zariski said (in his heavily accented Russo-Italian English) "In my time, I have had to learn many languages." At this, Grothendieck turned bright red.
		Another time Zariski was lecturing and Grothendieck again asked him why he didn't generalize his work to schemes.
	www.jmilne.org /math/apocrypha.html (627 words)

	The link of suspension singularities and Zariski's conjecture \| Department of Mathematics
		It is shown that some families of isolated hypersurface singularities have special and surprising properties.
		One of the consequences of the result is that one recovers the equisingular type of [g = 0] from its topology, in particular, (almost) all the analytic invariants of g.
		We also verify these results for a weighted homogeneous singularity whose link is a rational homology sphere.
	www.math.ohio-state.edu /node/150 (190 words)

	The Harvard Crimson :: News :: Adams, Price, Zariski to be Honored
		In addition, several sources indicated yesterday that former Secretary of State Cyrus Vance may be on this year's list of ten honorary degree recipients.
		Among his students, Zariski said, were David B. Mumford '57, who currently holds Zariski's former chair in mathematics, and Heisuke Hironake.
		Zariski, a specialist in algebraic geometry, was born in Russia, received his doctorate at the University of Rome, and came to the United States in 1927, "I feel a little bit uneasy talking about my achievements," he said, "but I never took mediocre students.
	www.thecrimson.com /article.aspx?ref=270013 (643 words)

	Springer Online Reference Works
		An abstract model of the category of commutative algebras (cf.
		The whole of basic commutative algebra and algebraic geometry can be formally developed in any Zariski category as if its objects were commutative rings.
		Any result proven in an arbitrary Zariski category has various interpretations in various concrete categories of commutative algebras of different kinds, possible equipped with some extra structure such as an order, lattice, gradation, filtration, differentiation, etc.
	eom.springer.de /z/z110010.htm (262 words)

	Zariski Topology
		The intersection of any finite collection of open sets is open.
		The Zariski topology is a different kind of topology.
		This confirms once again that the Zariski topology is much coarser than the analytic topology.)
	mathcircle.berkeley.edu /BMC3/alg-geom/node3.html (244 words)

	TL Forum 97: Zariski - lessons for teaching using group work from a survey of law students (Site not responding. Last check: 2007-10-15)
		TL Forum 97: Zariski - lessons for teaching using group work from a survey of law students
		This project was conducted jointly by the author and Associate Professor Gary Davis then of the Murdoch University Law School and now at Flinders University.
		Please cite as: Zariski, A. Lessons for teaching using group work from a survey of law students.
	lsn.curtin.edu.au /tlf/tlf1997/zariski.html (3022 words)

	Atlas: Globalization of an old Theorem of Zariski by Avinash Sathaye (Site not responding. Last check: 2007-10-15)
		Atlas: Globalization of an old Theorem of Zariski by Avinash Sathaye
		475-480), Zariski characterized plane unibranch curves having maximum torsion to be exactly curves of the form y
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caqm-87.
	atlas-conferences.com /cgi-bin/abstract/caqm-87 (280 words)

	The Mathematics Genealogy Project - Oscar Zariski
		Click here to see the students listed in chronological order.
		According to our current on-line database, Oscar Zariski has 15 students and 579 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.ams.org /html/id.phtml?id=18926 (78 words)

	Zariski Geometries (Site not responding. Last check: 2007-10-15)
		Danny Gillam will give the talk on Monday, April 4 at 4:15 in Math 528.
		Abstract: We address the following questions: Can a smooth curve be recovered solely by knowing the Zariski topology on each of its finite powers?
		What if we don't know the field it is defined over?
	www.math.columbia.edu /~welji/seminar/040405.html (123 words)

	TL Forum 2000: Zariski and Styles - enhancing student strategies for online learning (Site not responding. Last check: 2007-10-15)
		TL Forum 2000: Zariski and Styles - enhancing student strategies for online learning
		Zuckerman, M. The development of an affect adjective checklist for the measurement of anxiety.
		Please cite as: Zariski, A. and Styles, I. Enhancing student strategies for online learning.
	lsn.curtin.edu.au /tlf/tlf2000/zariski.html (3514 words)

	Electronic Law Journals - JILT 1998 (1) - Zariski (Site not responding. Last check: 2007-10-15)
		Electronic Law Journals - JILT 1998 (1) - Zariski
		Citation: Zariski A, 'Virtual Words and the Fate of Law', 1998 (1) The Journal of Information, Law and Technology (JILT).
		The life of the law increasingly is being lived in cyberspace, that new electronic environment created by the potential for communication amongst linked computer networks worldwide.
	www2.warwick.ac.uk /fac/soc/law/elj/jilt/1998_1/zariski (7350 words)

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