

Iskovskikh Seminar
March 23, 2017 18:00, Moscow, Steklov Mathematical Institute, room 540






Singularities of Cox rings and varieties of Fano/CalabiYau type
Sh. Okawa^{} ^{} Osaka University

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Abstract:
A smooth hypersurface of a projective space is either
Fano/CalabiYau/canonically polarized depending on its degree. These
three cases precisely correspond to the cases where the singularity of
the cone over the hypersurface is log terminal/(strictly) log
canonical/worse than log canonical.
I will give a generalization of this phenomena to Mori dream spaces, a
class of varieties which have very nice properties from the point of
view of the minimal model theory. In this generality, the cone over the
hypersurface will be generalized to the spectrum of the Cox ring of the
Mori dream space. This is a joint work with Yujiro Kawamata.

