Structure & Description

This mini course is combined with 2023 HDAG workshop. We will have 4 invited lecturers to give mini-courses of 3 lectures each. The topics of the mini-courses focus on derived geometry and birational geometry.

Talk Time (Agenda)

3/14 10:30-11:30

3/15 10:30-11:30

3/17 13:30-14:30

Abstract: Fano varieties with Picard number 1, or more generally Mori fiber spaces, is the most important class of spaces for the Minimal Model Program of rationally connected varieties. I will survey some classical and recent results in the case of threefolds, concentrating on rationality questions and the structure of derived categories of coherent sheaves.

Lecture I: Smooth Fano threefolds over an algebraically closed field (video)

Abstract: I will overview the classification of Fano threefolds of Picard number 1 over an algebraically closed field with an emphasis on rationality results and the structure of derived categories.

Lecture II: Smooth Fano threefolds over a nonclosed field (video)

Abstract: We will discuss the case of Fano threefolds over nonclosed fields and, more generally, smooth families of Fano threefolds over arbitrary base schemes. In particular, we will discuss rationality criteria for forms of geometrically rational Fano threefolds and the structure of their derived categories.

Lecture III: Conifold transitions (video)

Abstract: We will relate smooth del Pezzo threefolds of degree 1 le d le 5 to smooth prime Fano threefolds of genus g = 2d + 2 passing on the way through maximally nonfactorial nodal prime Fano threefolds. We will discuss some consequences of this construction to derived categories and categorical period maps.