, Sun Moon Lake Teachers Hotel

**Invited Speakers:**

Yujiro Kawamata (University of Tokyo& NCTS)

Yuan-Pin Lee (The University of Utah)

**Organizers:**

Jungkai Chen (National Taiwan University)

**Program**

13:00-13:50 Part1 of Kawamata

14:00-14:50 Part 2 of Kawamata

14:50-15:10 Coffee Break

15:10-16:00 Part 1 of Yuan-Pin

16:10-17:00 Part 2 of Yuan-Pin

**Title and Abstract**

Title: Curve counting and stable quotient

Speaker: Yuan-Pin Lee (Utah)

Abstract: I will give an introduction to curve counting. Then recent progress in counting curves via the stable quotients will be discussed, particularly the work of Lho and Pandharipande.

Title: Remarks on a theorem of Fujita.

Speaker: Yujiro Kawamata

Abstract:

The semi-positivity theorem states the following: let be a surjective morphism from a compact K"ahler manifold to a projective manifold whose fibers are connected. Assume that there are normal crossing divisors and on and , respectively, such that set-theoretically and such that is smooth on . Assume that the local monodromies are unipotent. Then is a locally free sheaf which is numerically semi-positive. A theorem of Fujita says that, if , then there is a decomposition , where is an ample vector bundle and $U$ has a unitary flat connection. A result by Catanese and Dettweiler states that there are many examples where is not semi-ample. I will explain these results and a generalization to the case where is arbitrary.

This is a joint work with Fabrizio Catanese.

**Contact:** Peggy Lee,peggylee@ncts.ntu.edu.tw, 02-3366-8815