**June 18-22, 2018 - ICTP Trieste**

## TAGSS II - Summer School on

Geometry of Moduli Spaces of Curves

Moduli spaces of stable pointed curves play an important role in
algebraic geometry.

The School had one course on vector bundles of coinvariants and on
conformal blocks and another one on their cohomology classes in
relation with those of moduli of abelian varieties.

About the first course, by A. Gibney: moduli spaces of curves carry
vector bundles of coinvariants and conformal blocks; they are
invariants of a curve C attached to a Lie group G that are
canonically isomorphic to global sections of an ample line bundle on
the moduli stack of certain G-bundles on C. These are generalized
theta functions in case C is smooth. In case g=0, the bundles of
co-invariants are globally generated, and their first Chern classes
are semi-ample line bundles on the moduli of curves, and shed light
on its birational geometry.

About the second course, by A. Tommasi: the cohomology of moduli
spaces of curves and abelian varieties carries several natural
classes. We focus on the tautological classes and the cohomology
classes related to spaces of modular forms. The problem of
determining relationships between the tautological classes turns out
to be particularly interesting.

The school featured courses by:

**Angela
Gibney** - University of Georgia

and

**Orsola
Tommasi** - Università di Padova