Complex Analytic and Differential Geometry
by Jean-Pierre Demailly
Publisher: Universite de Grenoble 2007
Number of pages: 571
From the table of contents: basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles and vanishing theorems, L2 estimates on pseudoconvex manifolds, q-convex spaces and Stein spaces.
Home page url
Download or read it online for free here:
by J.P. Murre - Tata Institute of Fundamental Research
The purpose of this text is to give an introduction to Grothendieck's theory of the fundamental group in algebraic geometry with the study of the fundamental group of an algebraic curve over an algebraically closed field of arbitrary characteristic.
by Olivia Dumitrescu, Motohico Mulase - arXiv
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the discovery of the relation between the topological recursion and the quantization of Hitchin spectral curves associated with Higgs bundles.
by William Fulton - Benjamin
These notes develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. It assumed that the reader is familiar with some basic properties of rings, ideals, and polynomials.
by Cumrun Vafa, Eric Zaslow - American Mathematical Society
The book provides an introduction to the field of mirror symmetry from both a mathematical and physical perspective. After covering the relevant background material, the monograph is devoted to the proof of mirror symmetry from various viewpoints.