Algebraic surfaces and holomorphic vector bundles pdf download

This book is a collection of survey articles by the main speakers at the symposium and presents to the mathematical world an overview of the key areas of research involving vector. Algebraic surfaces and holomorphic vector bundles universitext 9780387983615. Holomorphic vector bundles on nonalgebraic surfaces. Brussee, ontheunbalance of vector bundles on a blowup surface, preprint 1990. Some applications of vector bundles in algebraic geometry. 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. Algebraic surfaces and holomorphic vector bundles universitext 1. In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact riemann surfaces.

Grothendieck that algebraic vector bundles on the projective line are direct sums of line bundles. We describe the chern classes of holomorphic vector bundles on nonalgebraic complex torus of dimension 2. This book is based on courses given at columbia university on vector bun dles 1988 and on the theory of algebraic surfaces 1992, as well as lectures in the park city lias mathematics institute on 4manifolds and donald son invariants. The text for this class is acgh, geometry of algebraic curves, volume i. A note on holomorphic vector bundles over complex tori, nagoya math. We solve this problem in the case of rank 2 vector bundles over k3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class vii. We prove a topological criterion for the unstability of a vector bundle on a projective surface.

Then their refined chern classes satisy the duality ormula. The existence problem for holomorphic structures on vector bundles over nonalgebraic surfaces is. We are going to talk about compact riemann surfaces, which is the same thing. By serres gaga, the category of holomorphic vector bundles on a smooth complex projective variety x viewed as a complex manifold is equivalent to the category of algebraic vector bundles i. The goal of these lectures was to acquaint researchers in 4manifold topology with the classification of algebraic surfaces and with methods for.

Then we use it to study the pullbacks to x n and y n of bundles on p n. Algebraic surfaces and holomorphic vector bundles core. However, the study of algebraic surfaces and the moduli spaces of bundles on them remains a fundamen tal problem in algebraic geometry, and i hope that this. Featured on meta the q1 2020 community roadmap is on the blog. Coordinates for the universal moduli space of holomorphic. Deformation of vector bundles with holomorphic connections. Dolgachev,topics in classical algebraic geometry f r.

A moduli space of stable vector bundles on a smooth, algebraic variety x is a scheme whose points are in natural bijection to isomorphic classes of stable vector bundles on x. This is definitely false in the algebraic or holomorphic setting, even in dimension 1. We have attempted to give an informal presentation of the main results, addressed to a general audience. Algebraic surfaces and holomorphic vector bundles robert.

Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Complex algebraic surfaces download ebook pdf, epub. Hermitian vector bundles and the equidistribution of the. The existence problem for holomorphic structures on vector bundles over nonalgebraic surfaces is in general still open. To do this, we apply the theory of equivariant model maps developed in the paper. This content was uploaded by our users and we assume good faith they have the permission to share this book. Download it once and read it on your kindle device, pc, phones or tablets. Since its beginning in the twenties of this century, the theory of holomorphic endomorphisms of the riemann sphere rational functions has become well developed. In discussing chern classes it is also necessary to consider the category of di. Algebraic surfaces and holomorphic vector bundles universitext kindle edition by friedman, robert. E is called a holomorphic vector bundle over m if i are biholomorphic. The study of algebraic vector bundles of higher ranks began in 1957, when it was shown by a.

Kop algebraic surfaces and holomorphic vector bundles av robert friedman pa. Holomorphic vector bundles on nonalgebraic surfaces core. Friedman, algebraic surfaces and holomorphic vector bundles fu w. Use features like bookmarks, note taking and highlighting while reading algebraic surfaces and holomorphic vector bundles universitext. Algebraic surfaces and holomorphic vector bundles universitext kindle edition by robert friedman. Algebraic surfaces and holomorphic vector bundles pdf free. Topics in classical algebraic geometry algebraic surfaces. Im vaguely aware of the atiyah class, but are there other examples.

Coordinates for the universal moduli space of holomorphic vector bundles by j. Click download or read online button to get complex algebraic surfaces book now. Le potier, surexistence des fibres vectoriels holomorphes sur les surfaces, j. Symmetric powers of vector bundles on curves 257 restriction theorems 260 appendix. Most of our studies are concerned with algebraic vector bundles e with e e 1. Tropical lagrangian multisections and smoothing of locally free sheaves over degenerate calabiyau surfaces authors. The goal of these lectures was to acquaint researchers in 4manifold topology with the classification of algebraic surfaces and with methods for describing moduli spaces of holomorphic bundles on algebraic surfaces with a view toward computing donaldson invariants. Algebraic vector bundles on punctured affine spaces and. The 1993 durham symposium on vector bundles in algebraic geometry brought together some of the leading researchers in the field to explore further these interactions. Browse other questions tagged algebraicgeometry complexgeometry vectorbundles holomorphicbundles or ask your own question.

Vector bundle, algebraic encyclopedia of mathematics. The material presented here consists of a more or less selfcontained advanced course in complex algebraic geometry presupposing only some familiarity with the theory of algebraic curves or riemann surfaces. Sorry, we are unable to provide the full text but you may find it at the following locations. Let oeeeo be an exact sequence o holomorphic vectorbundles over x. As a side question, im curious what additional invariants one can construct for holomorphic vector bundles, which dont make sense for an ordinary complex vector bundle. Holomorphic vector bundles on primary kodaira surfaces. Given an algebraic vector bundle e on p n, e e is a nonnegative integer. Vector bundles in algebraic geometry enrique arrondo notes prepared for the first summer school on complex geometry villarrica, chile 79 december 2010 1. Some applications of vector bundles in algebraic geometry daniele faenzi. Vector bundles on algebraic varieties bombay, 1984, pp.

Pdf holomorphic vector bundles on primary kodaira surfaces. Algebraic surfaces and holomorphic vector bundle, i know what is a vector bundleor a fibre bundle in the differential geometry, but it seems that vector bundles in the algebraic geometry are something different, so who can tell me what is connection or difference between the two kinds of vector bundles, how. In this paper we study vector bundles on varieties of dimension greater than one. First we define an invariant e for algebraic vector bundles on p n. We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

A holomorphic line bundle is a rank one holomorphic vector bundle. Holomorphic vector bundles on nonalgebraic tori of. I am in trouble about the vector bundle part in the friedmans book. Algebraic surfaces and holomorphic vector bundles bokus. In order to discuss moduli of holomorphic vector bundles, it is essential to start with di. Are all vector bundles on a given vector bundle the pull back of a vector bundle on the base.