[PDF] Intersection Theory eBook

Author : W. Fulton
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 42,98 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662024217

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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.

Author : David Eisenbud
Publisher : Cambridge University Press
Page : 633 pages
File Size : 29,30 MB
Release : 2016-04-14
Category : Mathematics
ISBN : 1107017084

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3264, the mathematical solution to a question concerning geometric figures.

Author : William Fulton
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 29,97 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461217008

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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.

Author : William Fulton
Publisher : American Mathematical Soc.
Page : 98 pages
File Size : 35,30 MB
Release : 1984
Category : Mathematics
ISBN : 0821807048

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Introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. Suitable for graduate students in mathematics, this book describes the construction and computation of intersection products by means of the geometry of normal cones.

Author : Kenji Fukaya
Publisher : American Mathematical Soc.
Page : 426 pages
File Size : 31,71 MB
Release : 2010-06-21
Category : Mathematics
ISBN : 0821852507

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This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered $A_\infty$-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $A_\infty$ algebras and $A_\infty$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.

Author : Chris Wendl
Publisher : Cambridge University Press
Page : 197 pages
File Size : 45,68 MB
Release : 2020-03-26
Category : Mathematics
ISBN : 1108497403

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An accessible introduction to the intersection theory of punctured holomorphic curves and its applications in topology.

Author : Geir Ellingsrud
Publisher : Springer Science & Business Media
Page : 327 pages
File Size : 29,62 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461213169

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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.

Author : Laurenţiu G. Maxim
Publisher : Springer Nature
Page : 270 pages
File Size : 16,2 MB
Release : 2019-11-30
Category : Mathematics
ISBN : 3030276449

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This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Author : Terry A. McKee
Publisher : SIAM
Page : 213 pages
File Size : 50,87 MB
Release : 1999-01-01
Category : Mathematics
ISBN : 9780898719802

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Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics.

Author : Niva Piran
Publisher : Academic Press
Page : 338 pages
File Size : 19,79 MB
Release : 2017-09-15
Category : Psychology
ISBN : 0128094214

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Journeys of Embodiment at the Intersection of Body and Culture: The Developmental Theory of Embodiment describes an innovative developmental and feminist theory—understanding embodiment—to provide a new perspective on the interactions between the social environment of girls and young women of different social locations and their embodied experience of engagement with the world around them. The book proposes that the multitude of social experiences described by girls and women shape their body experiences via three core pathways: experiences in the physical domain, experiences in the mental domain and experiences related directly to social power. The book is structured around each developmental stage in the body journey of girls and young women, as influenced by their experience of embodiment. The theory builds on the emergent constructs of ‘embodiment’ and ‘body journey,’ and the key social experiences which shape embodiment throughout development and adolescence—from agency, functionality and passion during early childhood to restriction, shame and varied expressions of self-harm during and following puberty. By addressing not only adverse experiences at the intersection of gender, social class, ethnocultural grouping, resilience and facilitative social factors, the theory outlines constructive pathways toward transformation. It contends that both protective and risk factors are organized along these three pathways, with the positive and negative aspects conceptualized as Physical Freedom (vs. Corseting), Mental Freedom (vs. Corseting), and Social Power (vs. Disempowerment and Disconnection). Examines the construct of embodiment and its theoretical development Explores the social experiences that shape girls throughout development Recognizes the importance of the body and sexuality Includes narratives by girls and young women on how they inhabit their bodies Invites scholars and health professionals to critically reflect on the body journeys of diverse girls and women Addresses the advancement of feminist, social critical and psychological theory, as well as implications to practice—both therapy and health promotion