This e-book and the subsequent moment quantity is an creation into smooth algebraic geometry. within the first quantity the equipment of homological algebra, thought of sheaves, and sheaf cohomology are constructed. those tools are quintessential for contemporary algebraic geometry, yet also they are primary for different branches of arithmetic and of significant curiosity of their own.
within the final bankruptcy of quantity I those techniques are utilized to the idea of compact Riemann surfaces. during this bankruptcy the writer makes transparent how influential the tips of Abel, Riemann and Jacobi have been and that a few of the sleek tools were expected via them.
For this moment version the textual content was once thoroughly revised and corrected. the writer additionally further a brief part on moduli of elliptic curves with N-level buildings. This new paragraph anticipates a few of the suggestions of quantity II.
Read Online or Download Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics) PDF
Best Algebraic Geometry books
An available textual content introducing algebraic geometries and algebraic teams at complex undergraduate and early graduate point, this e-book develops the language of algebraic geometry from scratch and makes use of it to establish the idea of affine algebraic teams from first rules. development at the heritage fabric from algebraic geometry and algebraic teams, the textual content offers an creation to extra complex and specialized fabric.
The idea of elliptic curves is exceptional by way of its lengthy background and by means of the variety of the equipment which were utilized in its examine. This e-book treats the mathematics process in its sleek formula, by using uncomplicated algebraic quantity concept and algebraic geometry. Following a quick dialogue of the mandatory algebro-geometric effects, the publication proceeds with an exposition of the geometry and the formal staff of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.
This seriously class-tested publication is an exposition of the theoretical foundations of hyperbolic manifolds. it's a either a textbook and a reference. A simple wisdom of algebra and topology on the first 12 months graduate point of an American college is thought. the 1st half is anxious with hyperbolic geometry and discrete teams.
Additional info for Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics)