By Yang K.

A textbook for second-year graduate scholars who're acquainted with algebraic topology, functionality concept, and uncomplicated differential geometry. the gathering of seminar notes constitutes an creation to complicated algebraic geometry, concentrating on its transcendental element.

Show description

Read or Download Complex Algebraic Geometry: An Introduction to Curves and Surfaces PDF

Best algebraic geometry books

Geometric Models for Noncommutative Algebra

The quantity relies on a direction, "Geometric versions for Noncommutative Algebras" taught by way of Professor Weinstein at Berkeley. Noncommutative geometry is the research of noncommutative algebras as though they have been algebras of features on areas, for instance, the commutative algebras linked to affine algebraic forms, differentiable manifolds, topological areas, and degree areas.

Arrangements, local systems and singularities: CIMPA Summer School, Istanbul, 2007

This quantity includes the Lecture Notes of the CIMPA/TUBITAK summer season university preparations, neighborhood structures and Singularities held at Galatasaray collage, Istanbul in the course of June 2007. the amount is meant for a wide viewers in natural arithmetic, together with researchers and graduate scholars operating in algebraic geometry, singularity thought, topology and similar fields.

Algebraic Functions and Projective Curves

This booklet offers a self-contained exposition of the idea of algebraic curves with out requiring any of the must haves of recent algebraic geometry. The self-contained remedy makes this crucial and mathematically primary topic available to non-specialists. whilst, experts within the box should be to find numerous strange issues.

Riemannsche Flächen

Das vorliegende Buch beruht auf Vorlesungen und Seminaren für Studenten mittlerer und höherer Semester im Anschluß an eine Einführung in die komplexe Funktionentheorie. Die Theorie Riemannscher Flächen wird als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen research sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flächen aufzuklären und an vielen Beispielen und Bildern zu erläutern, die in der historischen Entwicklung eine Rolle spielten.

Extra info for Complex Algebraic Geometry: An Introduction to Curves and Surfaces

Example text

8) L e m m a . We have Horn(If(C, S), Alb(S)) = (0). P r o o f . If not, then K ( C , S) maps with finite kernel to AIb(S). Since we have E n d ( I f ( C , S)) = Z this implies by (3) that Jac(C) is rigid. But then S is a scroll or C is of genus zero, cf. 6, contrary to our assumption. [] 4. R e f e r e n c e s . : Geometry of algebraic curves I. Grundlehren der math. Wiss. 267. Springer Verlag1985. : Compact complex surfaces. F,rgebnisse der Mat12. 4. Springer Verlag, 1984. 40 [C] H. Clemens, J.

Therefore we assume that we have an endomorphism 77 of K~ defined over C(A). Using the curves P r we find that Dy - Dv, lies in the image of Pic(S) ~ Pic(C). Therefore we find that (13 - 7)(Y - Y') + T c ( y - y') e Image of Pic(S) --+ Pic(C). 3) that e lies in Z C End(K(C, S)) and this now proves that E n d ( K ( C , S)) = Z. The following lemma then finishes the proof of the Theorem. 8) L e m m a . We have Horn(If(C, S), Alb(S)) = (0). P r o o f . If not, then K ( C , S) maps with finite kernel to AIb(S).

A r) at P. - TL(G~(C,P,a)) is isomorphic to Ker(~o). r F Proof. By the completeness assumption on gd, Gd(C,P,a) is isomorphic, around r r the point [LI, to its image W~(C,P,a) in the jacobian of C. Hence T =TL(Gd(C,P,a)) is the same as the tangent space to the scheme %q~r (C,P,a) at the point corresponding to L. Recall that the deformations of the line bundle L correspond to the elements of HI(C,0c) in the following way. Take an affine covering {U h} of C over which L trivializes. Let {fhk} be the corresponding family of transition functions.

Download PDF sample

Rated 4.31 of 5 – based on 3 votes