Rational subvarieties in positive characteristic

October 24 to October 28, 2016

at the

American Institute of Mathematics, San Jose, California

organized by

Eric Riedl, Jason Starr, and Matthew Woolf

Original Announcement

This workshop will be devoted to studying rationality and existence of rational subvarieties in positive characteristic. Positive characteristic algebraic geometry provides additional tools, such as the Frobenius morphism, as well as challenges, such as the failure of generic smoothness. This workshop will bring together experts in both characteristic 0 and characteristic p to study questions related to rational varieties such as the following.

  1. When do the rational subvarieties of a Fano manifold, resp. general type variety, behave as expected from complex geometry?
  2. Which varieties of nonnegative Kodaira dimension are unirational, and what can we say about the moduli of these unirational varieties?
  3. How can we exploit positive characteristic methods to prove irrationality results, especially those results that lift to characteristic 0?

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

Normal bundles of rational curves on complete intersections
by  Izzet Coskun and Eric Riedl