
MAT 614 Syllabus
Curves on Algebraic Varieties
Fall 2011

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.

Week 1.
Castelnuovo's Contractibility Theorem and Uniruledness of Fano Manifolds.

Week 2. Overview of the Course and Toolkit for the Course.

Week 3.
Several Bend and Break Theorems.

Week 4.
The Cone Theorem and the Contraction Theorem (Smooth Case).

Week 5.
Cursory Overview of the Minimal Model Program.

Week 6.
Rationally Connected Varieties: Definitions and Foundational Results.

Week 7.
Rationally Connected Fibrations over Curves.

Week 8.
The Weak Approximation Problem: the HassettTschinkel Theorem.

Week 9.
Pseudosections and Extension of Sections from a Base Curve to a
Higherdimensional Base.

Week 10.
Ax's Conjecture and Rationally Connected Varieties over PAC Fields.

Week 11.
Rationally Simply Connected Varieties: Definitions and Main Examples.

Week 12.
Rational Simple Connectedness and the Weak Approximation Problem:
Hassett's Theorem.

Week 13.
Rationally Simply Connected Fibrations over Surfaces.

Week 14.
Applications and Rationally Simply Connected Varieties over Global
Function Fields / Function Fields over PAC Fields.
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Jason Starr
4108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 117943651
Phone: 6316328270
Fax: 6316327631
Jason Starr