MAT 614 Syllabus
Curves on Algebraic Varieties
What follows is a tentative syllabus. The pace of these topics (as well as
any additional topics to be covered) will be finalized in the first
weeks of the semester.
Castelnuovo's Contractibility Theorem and Uniruledness of Fano Manifolds.
Week 2. Overview of the Course and Toolkit for the Course.
Several Bend and Break Theorems.
The Cone Theorem and the Contraction Theorem (Smooth Case).
Cursory Overview of the Minimal Model Program.
Rationally Connected Varieties: Definitions and Foundational Results.
Rationally Connected Fibrations over Curves.
The Weak Approximation Problem: the Hassett-Tschinkel Theorem.
Pseudo-sections and Extension of Sections from a Base Curve to a
Ax's Conjecture and Rationally Connected Varieties over PAC Fields.
Rationally Simply Connected Varieties: Definitions and Main Examples.
Rational Simple Connectedness and the Weak Approximation Problem:
Rationally Simply Connected Fibrations over Surfaces.
Applications and Rationally Simply Connected Varieties over Global
Function Fields / Function Fields over PAC Fields.
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Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651