Lectures: tuesdays 13-15 in aula E and thursdays 8-10 in aula G.
WARNING: No class Thursday November 14.
Office hours: tuesdays 17:15 - 18:30, Dip.to di Matematica "G. Castelnuovo", office 137.
Classroom code: rsmb4tq
Outline of the course: The goal is to develop the theory of cohomology of sheaves on algebraic varieties, and to apply it to geometric problems.
In the first part of the course we will review (pre)sheaves, we will introduce (quasi)coherente sheaves on algebraic varieties, and their Cech
cohomology, we will prove basic finiteness results for cohomology groups of coeherent sheaves on projective varieties, and we will
give some geometric applications. Other goals: GAGA principle, Serre duality, the Riemann-Roch Theorem, applications to curves and surfaces.
References for the first part:
Andreas Gathmann: Algebraic Geometry 2021/22, Chapters 13-14-15-16, link
Ravi Vakil: Algebraic Geometry 2021/22, Part V, link
Marco Manetti: Geometria Superiore 2019/20, Capitolo 3 (in italian), link
Classnotes.
Sheaves-basic-notions link
Sheaves-of-modules link
(Quasi)Coherent-sheaves (2024-11-01) link
Cohomology of (quasi)coherent sheaves (2024-11-10) link
Homework.