# intersection-theory

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## Intersection Theory

**Author :**W. Fulton

**ISBN :**9783662024218

**Genre :**Mathematics

**File Size :**31. 14 MB

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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

**File Size :**46. 70 MB

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## Recent Progress In Intersection Theory

**Author :**Geir Ellingsrud

**ISBN :**081764122X

**Genre :**Mathematics

**File Size :**30. 77 MB

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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 :**

**File Size :**26. 61 MB

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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)

**File Size :**35. 94 MB

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## Intersection Theory On Surfaces

**Author :**Andrew Archibald

**ISBN :**OCLC:61568221

**Genre :**

**File Size :**45. 57 MB

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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

**File Size :**49. 72 MB

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## Intersection Theory And Separation Exponent In Complex Analytic Geometry

**Author :**Ewa Cygan

**ISBN :**OCLC:1225222222

**Genre :**

**File Size :**57. 7 MB

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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

**File Size :**71. 47 MB

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## Applications Of The Intersection Theory Of Singular Varieties

**Author :**Daniel Lowengrub

**ISBN :**OCLC:1066227873

**Genre :**

**File Size :**20. 75 MB

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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

**File Size :**57. 90 MB

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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 :**

**File Size :**35. 76 MB

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## Proceedings Of Symposia In Pure Mathematics

**Author :**

**ISBN :**UCAL:B5111406

**Genre :**Mathematics

**File Size :**41. 56 MB

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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

**File Size :**37. 29 MB

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## Enumerative Problems In Intersection Theory

**Author :**Astrid Adele Giugni

**ISBN :**OCLC:52758410

**Genre :**

**File Size :**28. 37 MB

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