Press "Enter" to skip to content

Download e-book for iPad: Algebraic Surfaces and Holomorphic Vector Bundles by Robert Friedman

By Robert Friedman

This ebook covers the speculation of algebraic surfaces and holomorphic vector bundles in an built-in demeanour. it truly is aimed toward graduate scholars who've had an intensive first-year path in algebraic geometry (at the extent of Hartshorne's Algebraic Geometry), in addition to extra complex graduate scholars and researchers within the components of algebraic geometry, gauge idea, or 4-manifold topology. some of the effects on vector bundles also needs to be of curiosity to physicists learning string thought. a unique function of the ebook is its built-in method of algebraic floor concept and the research of vector package deal concept on either curves and surfaces. whereas the 2 topics stay separate during the first few chapters, and are studied in trade chapters, they turn into even more tightly interconnected because the publication progresses. therefore vector bundles over curves are studied to appreciate governed surfaces, after which reappear within the evidence of Bogomolov's inequality for reliable bundles, that's itself utilized to check canonical embeddings of surfaces through Reider's approach. equally, governed and elliptic surfaces are mentioned intimately, after which the geometry of vector bundles over such surfaces is analyzed. a number of the effects on vector bundles look for the 1st time in e-book shape, compatible for graduate scholars. The e-book additionally has a robust emphasis on examples, either one of surfaces and vector bundles. There are over a hundred routines which shape a vital part of the textual content.

Show description

Read or Download Algebraic Surfaces and Holomorphic Vector Bundles PDF

Best algebraic geometry books

Jean-Pierre Serre's Abelian l-adic representations and elliptic curves PDF

This vintage e-book includes an advent to structures of l-adic representations, an issue of serious value in quantity idea and algebraic geometry, as mirrored via the striking fresh advancements at the Taniyama-Weil conjecture and Fermat's final Theorem. The preliminary chapters are dedicated to the Abelian case (complex multiplication), the place one unearths a pleasant correspondence among the l-adic representations and the linear representations of a few algebraic teams (now referred to as Taniyama groups).

Selected topics in algebraic geometry by Virgil Snyder PDF

This ebook resulted from stories (published in 1928 and 1932) of the Committee on Rational alterations, proven through the nationwide study Council. the aim of the studies used to be to offer a finished survey of the literature at the topic. every one bankruptcy is thought of as a separate unit that may be learn independently.

Curves and Abelian Varieties: International Conference March by Valery Alexeev, Arnaud Beauville, C. Herbert Clemens, Elham PDF

This ebook is dedicated to fresh growth within the learn of curves and abelian kinds. It discusses either classical features of this deep and lovely topic in addition to very important new advancements, tropical geometry and the idea of log schemes. as well as unique examine articles, this booklet comprises 3 surveys dedicated to singularities of theta divisors, of compactified Jacobians of singular curves, and of ""strange duality"" between moduli areas of vector bundles on algebraic types

Semidefinite optimization and convex algebraic geometry - download pdf or read online

This e-book presents a self-contained, obtainable creation to the mathematical advances and demanding situations because of using semidefinite programming in polynomial optimization. This fast evolving learn sector with contributions from the varied fields of convex geometry, algebraic geometry, and optimization is named convex algebraic geometry.

Extra info for Algebraic Surfaces and Holomorphic Vector Bundles

Example text

13 Digression: homeomorphism versus diffeomorphism. These constructions relate to two very profound questions in differentiable topology. The first question is: given a topological manifold, does it admit a smooth structure? Second: if it admits a smooth structure, is it then unique up to diffeomorphism? The second question was answered negatively by Milnor [35] (1957) who found an example of a smooth 7-manifold (called an exotic sphere) which is homeomorphic to the usual 7-sphere but not diffeomorphic to it.

So here comes the final, official definition of a cobordism: Let 0 and dism from 0 to maps 1 be closed oriented (n − 1)-manifolds. 2 Cobordisms 23 such that 0 maps diffeomorphically (preserving orientation) onto the inboundary of M, and 1 maps diffeomorphically (preserving orientation) onto the out-boundary of M. Note that this is practically the same as the first definition we gave, but it gives more flexibility. We can now have a a cobordism from to , provided we can find two diffeomorphisms: one from to the in-boundary, and another from to the out-boundary.

The precise categorical statement is that M0 pushout, or the colimit of M0 ← → M1 (cf. 7 in the Appendix). M1 → In the situation of the arbitrary diagram, the unique map f : M0 X can be thought of as the gluing of the two maps f0 and f1 . So the statement can also be formulated like this: continuous maps glue if they agree on the border between their domains. e. topological spaces equipped with atlases). 2 Gluing topological manifolds. Suppose now M0 and M1 are topological manifolds with a common boundary component .

Download PDF sample

Algebraic Surfaces and Holomorphic Vector Bundles by Robert Friedman


by Richard
4.0

Rated 4.77 of 5 – based on 49 votes