29/4, IMPA, sala 232. Nota que este dia é uma quarta-feira.
Positivity and moduli.|
Resumo. The ultimate aim of this lecture is to explain recent results, joint with
Zsolt Patakfalvi, on projectivity of moduli spaces of stable log-varieties
of general type and on Iitaka's conjecture regarding subadditivity of
log-Kodaira dimension for fiber spaces. On route to discussing these new
results I will review background material on moduli spaces and positivity
as well as previous results on projectivity of moduli spaces and on
Iitaka's conjecture. The central tools of the proofs are a strengthening of
Kollár's celebrated Ampleness Lemma and its application to pushforwards of
relative pluricanonical sheaves and their determinants. Time permitting I
will explain the essentials of this approach without getting into technical
Sandra Di Rocco,
Toric vector bundles and polytopes. |
Resumo. We will motivate and define the category of toric vector bundles over smooth complete toric varieties. After highlighting some applications and potential applications, we will concentrate on extending various properties of line bundles on smooth toric varieties to higher-rank toric vector bundles. Klaychko’s characterization of toric vector bundles intrinsically carries the definition of associated polytopes, extending the corresponding theory of line bundles. Positivity properties, as global generation and generation of jets, are visualised in terms of convex properties of the corresponding polytopes and provide useful criteria. I will illustrate this correspondence and show how these criteria lead to proving and disproving connections between various notions of positivity and cohomology vanishing. This is joint work with G. Smith and K. Jabbusch.