intersection-theory

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Intersection Theory

Author : W. Fulton
ISBN : 9783662024218
Genre : Mathematics
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From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cen turies, intersection theory has played a central role. Since its role in founda tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive his tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to devel op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appen dices. Some of the examples, and a few of the later sections, require more spe cialized knowledge. The text is designed so that one who understands the con structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should fa cilitate use as a reference.

Intersection Theory

Author : William Fulton
ISBN : 9781461217008
Genre : Mathematics
File Size : 86. 85 MB
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Intersection theory has played a central role in mathematics, from the ancient origins of algebraic geometry in the solutions of polynomial equations to the triumphs of algebraic geometry during the last two centuries. This book develops the foundations of the theory and indicates the range of classical and modern applications. The hardcover edition received the prestigious Steele Prize in 1996 for best exposition.

Introduction To Intersection Theory In Algebraic Geometry

Author : William Fulton
ISBN : 9780821807040
Genre : Mathematics
File Size : 68. 25 MB
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This book introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. It requires little technical background: much of the material is accessible to graduate students in mathematics. A broad survey, the book touches on many topics, most importantly introducing a powerful new approach developed by the author and R. MacPherson. It was written from the expository lectures delivered at the NSF-supported CBMS conference at George Mason University, held June 27-July 1, 1983.The author describes the construction and computation of intersection products by means of the geometry of normal cones. In the case of properly intersecting varieties, this yields Samuel's intersection multiplicity; at the other extreme it gives the self-intersection formula in terms of a Chern class of the normal bundle; in general it produces the excess intersection formula of the author and R. MacPherson. Among the applications presented are formulas for degeneracy loci, residual intersections, and multiple point loci; dynamic interpretations of intersection products; Schubert calculus and solutions to enumerative geometry problems; and Riemann-Roch theorems.

Intersection Theory In Grassmann Varieties

Author : Aigli Helen Papantonopoulou
ISBN : UCAL:C3512607
Genre :
File Size : 27. 86 MB
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An Extension Of The Lefschetz Intersection Theory

Author : Madeline Levin
ISBN : UCAL:B4250761
Genre : Topology
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Recent Progress In Intersection Theory

Author : Geir Ellingsrud
ISBN : 081764122X
Genre : Mathematics
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The articles in this volume are an outgrowth of an International Confer­ ence in Intersection Theory that took place in Bologna, Italy (December 1997). In a somewhat unorthodox format aimed at both the mathematical community as well as summer school students, talks were research-oriented as well as partly expository. There were four series of expository talks by the following people: M. Brion, University of Grenoble, on Equivariant Chow groups and applications; H. Flenner, University of Bochum, on Joins and intersections; E. M. Friedlander, Northwestern University, on Intersection products for spaces of algebraic cycles; R. Laterveer, University of Strasbourg, on Bigraded Chow (co)homology. Four introductory papers cover the following topics and bring the reader to the forefront of research: 1) the excess intersection algorithm of Stuckrad and Vogel, combined with the deformation to the normal cone, together with many of its geo­ metric applications; 2) new and very important homotopy theory techniques that are now used in intersection theory; 3) the Bloch-Beilinson filtration and the theory of motives; 4) algebraic stacks, the modern language of moduli theory. Other research articles concern such active fields as stable maps and Gromov-Witten invariants, deformation theory of complex varieties, and others. Organizers of the conference were Rudiger Achilles, Mirella Manaresi, and Angelo Vistoli, all from the University of Bologna; the scientific com­ mittee consisted of Geir Ellingsrud, University of Oslo, William Fulton, University of Michigan at Ann Arbor, and Angelo Vistoli. The conference was financed by the European Union (contract no.

Intersection Theory

Author : Jacob James Keller
ISBN : OCLC:1107111399
Genre :
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This thesis is intended to give an introduction to intersection theory in algebraic geometry. It is split into three chapters concerning the Chow ring, Schubert Calculus, and Chern classes respectively. It is intended to give the reader a toolkit with which to attack various enumerative problems arising from algebraic geometry. These problems include counting the points in an intersection of two varieties or counting the number of lines contained in a variety, and are central to many facets of modern algebraic geometry.

Intersection Theory Divisors

Author : William Fulton
ISBN : LCCN:97048781
Genre : Intersection theory (Mathematics)
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Intersection Theory On Surfaces

Author : Andrew Archibald
ISBN : OCLC:61568221
Genre :
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"This thesis studies intersection theory on projective surfaces with isolated singularities. We review the classical intersection theory on a nonsingular surface, proceed to an overview of types of singularity that may arise, and then discuss the intersection theory of Snapper-Kleiman, that of Reeve-Tyrrell, and a modification of the latter that we propose." --

Intersection Theory

Author : William Fulton
ISBN : UOM:49015000693219
Genre : Mathematics
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Intersection Theory And Separation Exponent In Complex Analytic Geometry

Author : Ewa Cygan
ISBN : OCLC:1225222222
Genre :
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Conical Intersections

Author : Wolfgang Domcke
ISBN : 9789814313452
Genre : Science
File Size : 70. 13 MB
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Pt. I. Fundamental aspects and electronic structure. 1. Conical intersections in organic photochemistry / M. A. Robb. 2. Efficient excited-state deactivation in organic chromophores and biologically relevant molecules: role of electron and proton transfer processes / A. L. Sobolewski and W. Domcke. 3. Three-state conical intersections / S. Matsika. 4. Spin-orbit vibronic coupling in Jahn-Teller systems / L. V. Poluyanov and W. Domcke. 5. Symmetry analysis of geometric-phase effects in quantum dynamics / S. C. Althorpe -- pt. II. Dynamics at conical intersections. 6. Conical intersections in electron photodetachment spectroscopy: theory and applications / M. S. Schuurman and D. R. Yarkony. 7. Multistate vibronic dynamics and multiple conical intersections / S. Faraji, S. Gomez-Carrasco and H. Koppel. 8. Conical intersections coupled to an environment / I. Burghardt ... [et al.]. 9. Ab initio multiple spawning: first principles dynamics around conical intersections / S. Yang and T. J. Martinez. 10. Non-Born-Oppenheimer molecular dynamics for conical intersections, avoided crossings, and weak interactions / A. W. Jasper and D. G. Truhlar. 11. Computational and methodological elements for nonadiabatic trajectory dynamics simulations of molecules / M. Barbatti, R. Shepard and H. Lischka. 12. Nonadiabatic trajectory calculations with ab initio and semiempirical methods / E. Fabiano ... [et al.]. 13. Multistate nonadiabatic dynamics "on the fly" in complex systems and its control by laser fields / R. Mitric, J. Petersen and V. Bonacic-Koutecky. 14. Laser control of ultrafast dynamics at conical intersections / Y. Ohtsuki and W. Domcke -- pt. III. Experimental detection of dynamics at conical intersections. 15. Exploring nuclear motion through conical intersections in the UV photodissociation of azoles, phenols and related systems / T. A. A. Oliver ... [et al.]. 16. Interrogation of nonadiabatic molecular dynamics via time-resolved photoelectron spectroscopy / M. S. Schuurman and A. Stolow. 17. Pump-probe spectroscopy of ultrafast vibronic dynamics in organic chromophores / N. K. Schwalb ... [et al.]. 18. Femtosecond pump-probe polarization spectroscopy of vibronic dynamics at conical intersections and funnels / W. K. Peters, E. R. Smith and D. M. Jonas

Nielsen Theory And Reidemeister Torsion

Author : Jerzy Jezierski
ISBN : UOM:39015042596620
Genre : Fixed point theory
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Applications Of The Intersection Theory Of Singular Varieties

Author : Daniel Lowengrub
ISBN : OCLC:1066227873
Genre :
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We develop tools for computing invariants of singular varieties and apply them to the classical theory of nodal curves and the complexity analysis of non-convex optimization problems. The first result provides a method for computing the Segre class of a closed embedding X → Y in terms of the Segre classes of X and Y in an ambient space Z. This method is used to extend the classical Riemann-Kempf formula to the case of nodal curves. Next we focus on techniques for computing the ED degree of a complex projective variety associated to an optimization problem. As a first application we consider the problem of scene reconstruction and find a degree 3 polynomial that computes the ED degree of the multiview variety as a function of the number of cameras. Our second application concerns the problem of weighted low rank approximation. We provide a characterization of the weight matrices for which the weighted 1-rank approximation problem has maximal ED degree.

Methods Of Algebraic Geometry Book 3 General Theory Of Algebraic Varieties In Projective Space Book 4 Quadrics And Grassmann Varieties

Author : William Vallance Douglas Hodge
ISBN : UCAL:B4074006
Genre : Geometry, Algebraic
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Proceedings Of The International Congress Of Mathematicians August 21 29 1990 Kyoto Japan

Author : Ichirō Satake
ISBN : 0387700471
Genre : Mathematics
File Size : 78. 33 MB
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Intersection Theory On Tropical Toric Varieties And Compactifications Of Tropical Parameter Spaces

Author : Henning Meyer
ISBN : OCLC:1184295811
Genre :
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Proceedings Of Symposia In Pure Mathematics

Author :
ISBN : UCAL:B5111406
Genre : Mathematics
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Abstracts Of Theses Accepted In Partial Fulfillment Of The Requirements For The Doctor S Degree

Author : Massachusetts Institute of Technology
ISBN : PSU:000060139238
Genre : Dissertations, Academic
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Enumerative Problems In Intersection Theory

Author : Astrid Adele Giugni
ISBN : OCLC:52758410
Genre :
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