By Robert Friedman

This publication covers the idea of algebraic surfaces and holomorphic vector bundles in an built-in demeanour. it's aimed toward graduate scholars who've had an intensive first-year direction 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 conception, or 4-manifold topology. some of the effects on vector bundles also needs to be of curiosity to physicists learning string conception. a unique characteristic of the publication is its built-in method of algebraic floor idea and the research of vector package deal concept on either curves and surfaces. whereas the 2 matters stay separate during the first few chapters, and are studied in exchange chapters, they turn into even more tightly interconnected because the e-book progresses. therefore vector bundles over curves are studied to appreciate governed surfaces, after which reappear within the facts of Bogomolov's inequality for strong bundles, that's itself utilized to check canonical embeddings of surfaces through Reider's technique. equally, governed and elliptic surfaces are mentioned intimately, after which the geometry of vector bundles over such surfaces is analyzed. a few of the effects on vector bundles seem 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 Online or Download Algebraic Surfaces and Holomorphic Vector Bundles PDF

Similar algebraic geometry books

The legacy of Niels Henrik Abel: the Abel bicentennial, - download pdf or read online

This e-book features a sequence of analysis papers on topics on the topic of the paintings of Niels Henrik Abel, written via the various top-rated experts of their fields. a number of the authors were in particular invited to give papers, discussing the impact of Abel in a mathematical-historical context.

Download e-book for kindle: Tata Lectures on Theta III by David Mumford, M. Nori, P. Norman

The second one in a chain of 3 volumes surveying the idea of theta capabilities, this quantity supplies emphasis to the distinctive homes of the theta capabilities linked to compact Riemann surfaces and the way they result in ideas of the Korteweg-de-Vries equations in addition to different non-linear differential equations of mathematical physics.

Download e-book for kindle: Logarithmic forms and diophantine geometry by A. Baker, G. Wüstholz

There's now a lot interaction among reviews on logarithmic varieties and deep features of mathematics algebraic geometry. New mild has been shed, for example, at the well-known conjectures of Tate and Shafarevich with regards to abelian types and the linked celebrated discoveries of Faltings developing the Mordell conjecture.

Mostly surfaces by Richard Evan Schwartz PDF

This booklet offers a few issues regarding surfaces, corresponding to Euclidean, round and hyperbolic geometry, the elemental workforce, common overlaying surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. the most concept is to get to a couple attention-grabbing arithmetic with out an excessive amount of formality.

Extra resources for Algebraic Surfaces and Holomorphic Vector Bundles

Example text

Let R be a graded k-algebra such that char(k) = and there is a k-derivation D: R ----+ R of weight -1 and an element t E RI with the property that D(t) = 1. If A := {r E R I D(r) = O}, then A is a graded k-subalgebra of R, t is transcendental over A and R = A[t]. Moreover, D = -it on A[t]. Proof. The fact that A is a graded k-subalgebra of R is immediate. Let A[T] be the polynomial A-algebra in the indeterminate T. Grade A[T] by deg(aTm) = deg( a) + m for every a E A homogeneous and m 2: 0. Consider the homomorphism of graded k-algebras rp: A[T] ----+ R such that rplA = idA and rp(T) = t.

Replacing h, ... ,1s by h, h - adl' fs - ash, we may therefore assume that

This shows that (X, L) is a smooth polarized variety of dimension 2:: 3 (which is not a cone), such that HO(X, Tx ® L -1) i= 0. ° A Counterexample in Characteristic 3 Let k be an algebraically closed field of characteristic 3. In JP>3 consider the surface X of equation f = T5 + T1Ti + T2T; + T3 T * f. £ We have = 0, = Ti + 2T1 T 3 = Ti - T1T3, T'f - T 2T 3· The closed subvariety in]p>3 of equations *k = Tj- T1T2, Tl- T2 T 3 = Ti - T1 T 3 = T;- T1T2 = * ° is (at least set-theoretically) the line as one can easily see.

Download PDF sample

Algebraic Surfaces and Holomorphic Vector Bundles by Robert Friedman


by Paul
4.4

Rated 4.85 of 5 – based on 7 votes