ADVANCED GEOMETRY 2
Learning outcomes of the course unit
Learn basic notions on complex analysis in several variables.
Holomorphic functions of one complex variable.
Course contents summary
Holomorphic functions of several variables. Stein spaces. Sheaf theory and sheaf cohomology.
Holomorphic functions of several variables (Hartogs' Teorem, Weierstrass' Theorems, Riemann' extension Theorem, Nullstellensatz). Sheaf theory and sheaf cohomology (rudiments of homological algebra, abstract de Rham Theorem, de Rham and Dolbeault Theorems). Stein spaces.
Giuseppe Della Sala, Alberto Saracco, Alexandru Simioniuc and Giuseppe Tomassini, Lectures on complex analysis and analytic geometry, Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)] 3, Edizioni della Normale, Pisa (2006), xx+430.
Standard blackboard lectures.
Assessment methods and criteria
Homeworks during the course. Final exam will be an expository talk on a subject assigned by the theacher.