Geometry

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• Lorenzo Barban (Università di Trento)

March 23rd, 2022, 14:00 (aula Seminari -1 Povo0 e zoom)

Title: Mori dream regions and C*-actions

Abstract:

The notion of Mori dream region (MDR for short) has been introduced by Y. Hu and S. Keel as a generalization of Mori dream spaces. In this talk we establish a correspondence between MDR associated to small Q-factorial modifications and certain C*-actions on polarized pairs (X,L), with X normal projective and L ample and C*-linearizable, called bordisms. This talk is based on a joint work in progress with E. A. Romano (University of Genova), L. E. Solá Conde (University of Trento), and S. Urbinati (University of Udine).

• Klaus Altmann (Freie Universität Berlin)

April 6th, 2022, 14:00 (aula Seminari -1 Povo0 e zoom)

Title: The structure of exceptional sequence on toric varieties of Picard rank two

Abstract:

For a smooth projective toric variety of Picard rank two we classify all exceptional sequences of invertible sheaves which have maximal length. In particular, we prove that unlike non-maximal sequences, they

(a) remain exceptional under lexicographical reordering

(b) satisfy strong height constraints in the Picard lattice

(c) are full, that is, they generate the derived category of the variety.

Moreover, we determine the exceptional poset of those sequences and show how this poset governs the property "strongly exceptional".

(This is joint work with Frederik Witt, Stuttgart; see arXiv:2112.14637 [math.AG])

• We organized the workshop: "Newton-Okounkov bodies and Fanosearch". Levico Terme, October 5-8, 2021. Further information here.

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