# Seminario di Geometria: Geometric properties of projective manifolds of small degree (Park)

## Dettagli dell'evento

### Quando

09/12/2014
dalle 15:30 alle 16:30

### Dove

Aula 1, Dipartimento di Matematica e Informatica

### Aggiungi l'evento al calendario

Il Dott. Jinhyung Park del KIAS (Seul) sara ospite del nostro Dipartimento nel periodo 9-16 Dicembre.

L'invitato terra due seminari:

Primo seminario, Martedi 9 Dicembre, ore 15.30-16.30, aula 1.

Geometric properties of projective manifolds of small degree

Abstract: In this talk, we study geometric structures of projective manifolds of small degree from birational geometric viewpoints. First, using the positivity properties of double point divisors and Castelnuovo's bound on sectional genus, we prove that almost every projective manifold in r-dimensional projective space of degree d < r+3 is rationally connected. We also show the finite generation of Cox rings of projective manifolds of degree d < r+1 with counter-examples for d = r+1, r+2. On the other hand, using the concavity theorem and Harris' classification of Castelnuovo varieties, we show that every n-dimensional projective manifold of degree d < n(r-n)+3 is either uniruled or Calabi-Yau. This is joint work with Sijong Kwak.

Secondo seminario, Giovedi 11 Dicembre, ore 11-12, aula 1.

Anticanonical models and maps of Fano type varieties

Tutti gli interessati sono invitati a partecipare.

Paltin Ionescu