Rational curves on algebraic varieties

May 7 to May 11, 2007

at the

American Institute of Mathematics, Palo Alto, California

organized by

Brendan Hassett and Sandor Kovacs

Original Announcement

This workshop will be devoted to rationally-connected varieties. The original impetus for studying these varieties came from classification theory, and many central problems in this area remain open: Are all rationally-connected varieties unirational? Is there a rational surface passing through the generic point on a rationally connected variety? If not, what positivity hypotheses might guarantee the existence of such surfaces?

At the same time, techniques developed for studying rationally-connected varieties have found wide application in algebraic and arithmetic geometry. The workshop will focus on the following tools:

One main goal will be to present and discuss state-of-the-art techniques in each of these areas. We expect that a better grasp of these methods should yield new insights into classification questions and a deeper understanding of Diophantine properties of rationally-connected varieties over local and function fields.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.