#
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:

- deformation theory of curves and combs
- constructions of free curves with desired properties
- moduli spaces of stable maps
- singularity theory and rational-chain connectedness

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: