ERC Research Period on Diophantine Geometry
timetable:
Wed 10 Oct, 11:20 - 12:00, Sala Conferenze Centro De Giorgi
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Arithmetic positivity on toric varieties (40')
speaker: Martin Sombra (ICREA and Universitat de Barcelona)abstract: There is a dictionary between the algebro-geometric properties of toric varieties and the combinatorial properties of lattice polytopes and fans. This dictionary can be extended to relate the Arakelov theory of toric varieties with convex analysis In this talk, I will explain some recent additions to this dictionary concerning arithmetic positivity. In particular, I will give criteria for positivity of metrized line bundles on toric varieties, formulae for the arithmetic volume of a toric variety, a generalization of Dirichlet's units theorem to toric varieties, and a criterion for the existence of an equivariant Zariski decomposition. This is joint work with J. I. Burgos, A. Moriwaki and P. Philippon.
timetable:
Wed 10 Oct, 11:20 - 12:00, Sala Conferenze Centro De Giorgi
<< Go back