3 edition of **Vector bundles on algebraic varieties** found in the catalog.

Vector bundles on algebraic varieties

- 178 Want to read
- 5 Currently reading

Published
**1987**
by Oxford University Press, Published for the Tata Institute of Fundamental Research, Bombay in Bombay
.

Written in English

- Vector bundles -- Congresses,
- Algebraic varieties -- Congresses

**Edition Notes**

Statement | by Atiyah ... [et al.] |

Series | Tata Institute of Fundamental Research studies in mathematics : -- v. 11, Studies in mathematics (Tata Institute of Fundamental Research) -- 11 |

Contributions | Atiyah, Michael Francis, 1929-, Tata Institute of Fundamental Research, International Colloquium on Vector Bundles on Algebraic Varieties (1984 : Tata Institute of Fundamental Research) |

The Physical Object | |
---|---|

Pagination | vi, 555 p. ; |

Number of Pages | 555 |

ID Numbers | |

Open Library | OL14635653M |

ISBN 10 | 195620143 |

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in , Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In he moved to California where he is now Professor at the University of California at Berkeley.4/5(10). and the study of vector bundles could be called Linear Algebraic Topology. The only two vector bundles with base space a circle and one-dimensional ﬁber are the M¨obius band and the annulus, but the classiﬁcation of all the d iﬀerent vector bundles over a given base space with ﬁber of a given dimension is quite diﬃcult in general.

during the school entitled "School on vector bundles and low codimensional subvarieties", held at CIRM, Trento, (Italy), during the period September , In no case do I claim it is a survey on moduli spaces of vector bundles on algebraic projective varieties. Many people have made important contributions without even being mentioned. Synopsis The Bayreuth meeting on "Complex Algebraic Varieties" focused on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference Format: Perfect Paperback.

Aug 15, · In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors, of compactified Jacobians of singular curves, and of “strange duality” among moduli spaces of vector bundles on algebraic varieties. May 14, · RIMS preprint () # Conterexample to Hilbert's fourteenth problem for the 3-dimensional additive group, # Geometric realization of T-Shaped root systems and counterexamples to Hilbert's fourteenth problem, (Algebraic Transformation Group and Algebraic Varieties, pp, Springer Verlag, Berlin, ).

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In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the.

Buy Vector Bundles on Algebraic Varieties: Papers presented at the Bombay Colloquium (TATA INSTITUTE OF FUNDAMENTAL RESEARCH, BOMBAY// STUDIES IN MATHEMATICS) on runrevlive.com FREE SHIPPING on qualified ordersCited by: 1. The first part tackles the classification of vector bundles on algebraic curves.

The author also discusses the construction and elementary properties of the moduli spaces of stable bundles. In particular Le Potier constructs HilbertSHGrothendieck schemes of vector bundles, Author: J. Le Potier. In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.

The definition of coherent sheaves is made with reference to a sheaf of rings that codifies this geometric information.

Coherent sheaves can be seen as a generalization of vector bundles. The aim of the colloquium was to highlight recent developments in the general area of vector bundles as well as principal bundles of both affine and projective varieties. The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry.

Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. The case of a projective base. The study of line bundles on projective varieties is a classical problem in algebraic geometry (cf. Picard group; Picard scheme).The study of algebraic vector bundles of higher ranks began inwhen it was shown by A.

Grothendieck that algebraic vector bundles on the projective line are direct sums of line bundles. It is an additional structure which belongs to the vector bundle. The modern definition of a vector bundle (which works for manifolds, analytic spaces and schemes at once, in fact arbitrary ringed spaces) is that of a locally free sheaf of modules.

Actually this definition simplifies lots of. Vector bundles in Algebraic Geometry Enrique Arrondo Notes(*) prepared for the First Summer School on Complex Geometry (Villarrica, Chile December ) 1. The notion of vector bundle In a ne geometry, a ne varieties are de ned by zeros of polynomials in the sense that.

The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference.

Questions on Algebraic Varieties. Editors; E. Marchionna; Book. 32 Search within book. Front Matter. Pages i-iii. PDF. Residus et Courants.

Hauteurs et théorie des intersections.- A. Seidenberg: Report on analytic product.- C.S. Seshadri: Moduli of p-vector bundles over an algebraic curve.- O. Zariski: Contributions to the problem of. "International Colloquium on Vector Bundles on Algebraic Varieties, held at the Tata Institute of Fundamental Research in January, "--Page 4 of cover.

Description: vi, pages:. The study of vector bundles over algebraic varieties has been stimulated over the last few years by successive waves of migrant concepts, largely from mathematical physics, whilst retaining its roots in old questions concerning subvarieties of projective space.

Dear Mohammad, there is a rather elementary book Introduction to Moduli Problems and Orbit spaces by P.E. Newstead which will explain to you why stability is important, give you lots of examples (Chapter 4 is devoted to them) and which ends with a whole chapter (Chapter 5) called Vector bundles over a runrevlive.com was written by an extremely competent expert and deliberately maintained at a quite.

Analytic Cycles and Vector Bundles on Non-Compact Algebraic Varieties 3 in the case of line bundles), we are able to give a new proof of Grauert's theorem based on the LZ-methods for the 0-operator and a certain lineari- zation trick (w 19 and 20), a proof which does give some growth conditions.

This book offers a systematic treatment of the theory of vector bundles with integrable connection on smooth algebraic varieties over a field of characteristic 0. The authors develop a new approach to classical algebraic/analytic comparison theorems in De Rham cohomology.

it and refer back to it as needed (page-references are used throughout the book to facilitate this). It ends with a brief treatment of category theory. Appendix B on page is an introduction to sheaves, in preparation for structure sheaves of schemes and general varieties.

It also develops the theory of vector-bundles over an afﬁne variety. He is the author of "Residues and Duality" (), "Foundations of Projective Geometry (), "Ample Subvarieties of Algebraic Varieties" (), and numerous research titles.

His current research interest is the geometry of projective varieties and vector bundles. Endomorphism algebras for abelian varieties over finite fields follow from the theory of Tate.

The chapter presents some general facts and related theorems concerning endomorphism algebras. This chapter presents a construction method of algebraic vector bundles on noetherian schemes X by analyzing The book concludes with an assessment.

What are the open big problems in algebraic geometry and vector bundles. More specifically, I would like to know what are interesting problems related to moduli spaces of. Vector Bundles in Algebraic Geometry | Successive waves of migrant concepts, largely from mathematical physics, have stimulated the study of vector bundles over algebraic varieties in the past few years.

But the subject has retained its roots in old questions concerning subvarieties of projective space.The next topic that we will treat is a particular class of vector bundles (or sheaves), namely arithmetically Cohen-Macaulay (ACM) and Ulrich sheaves, tra- ditionally important in commutative algebra and representation theory of rings.The structure group then acts as a matrix transformation between vector components, and between bases in the opposite direction.

A gauge transformation is also a new choice of basis, and so can be handled similarly. A vector bundle always has global sections (e.g. the zero vector in .