Lectures on Birational Geometry
by Caucher Birkar
Publisher: arXiv 2012
Number of pages: 85
Lecture notes of a course on birational geometry. Topics covered: introduction into the subject, contractions and extremal rays, pairs and singularities, Kodaira dimension, minimal model program, cone and contraction, vanishing, base point freeness, flips and local finite generation, pl flips and extension theorems, existence of minimal models and Mori fibre spaces, global finite generation, etc.
Home page url
Download or read it online for free here:
by Tadao Oda - Springer
The theory of toric varieties describes a fascinating interplay between algebraic geometry and the geometry of convex figures in real affine spaces. This book is a unified up-to-date survey of the various results and interesting applications ...
by J. S. Milne
Introduction to both the geometry and the arithmetic of abelian varieties. It includes a discussion of the theorems of Honda and Tate concerning abelian varieties over finite fields and the paper of Faltings in which he proves Mordell's Conjecture.
by H. Maass - Tata Institute of Fundamental Research
Contents: Modular Group of Degree n; Symplectic group of degree n; Reduction Theory of Positive Definite Quadratic Forms; Fundamental Domain of the Modular Group of Degree n; Modular Forms of Degree n; Algebraic dependence of modular forms; etc.
by Armand Borel, George D. Mostow - American Mathematical Society
The book covers linear algebraic groups and arithmetic groups, adeles and arithmetic properties of algebraic groups, automorphic functions and spectral decomposition of L2-spaces, vector valued cohomology and deformation of discrete subgroups, etc.