Rational curves on algebraic varieties

May 7 to May 11, 2007

at the

American Institute of Mathematics, San Jose, 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.

Papers arising from the workshop:

Rigidity of Mori cone for Fano manifolds
by  Jaroslaw A. Wisniewski
Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces
by  Brendan Hassett and Yuri Tschinkel
Moving and ample cones of holomorphic symplectic fourfolds
by  Brendan Hassett and Yuri Tschinkel
Log Fano varieties over function fields of curves
by  Brendan Hassett and Yuri Tschinkel
Congruence for rational points over finite fields and coniveau over local fields
by  Hélène Esnault and Chenyang Xu.