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Seminario / Keum

SEMINARIO DI GEOMETRIA ALGEBRICA

Nell'ambito del seminario congiunto di geometria algebrica organizzato
dai Dipartimenti di Matematica dell'Università e del Politecnico di Milano,

lunedì 26 Settembre alle 14:00 (durata 1 ora)

in Aula C del Dipartimento di Matematica "F. Enriques", si terrà il seguente seminario:

JongHae Keum
(KIAS)

Mori dream surfaces


Abstract: The Cox ring of a variety is the total coordinate ring, i.e., the direct sum of all spaces of global sections of all divisors.
When this ring is finitely generated, the variety is called Mori dream (MD). A necessary condition for being MD is the finite generatedness of Pic(X), i.e., the vanishing of the irregularity.
Smooth rational surfaces with big anticanonical divisor are MD. Thus all del Pezzo surfaces of any degree are.
A K3 surface or an Enriques surface is MD iff its automorphism group is finite.
In this talk I will consider the case of surfaces of general type with p_g=0, and provide several examples that are MD. I will also provide non-minimal examples that are not MD.
This is a joint work with Kyoung-Seog Lee.

23 settembre 2022
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