16 oct 2019 -- 14:00
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
I will discuss joint work in progress with Enrico Schlitzer (SISSA). We introduce a new system of partial differential equations that describe special metrics on pairs formed by a Kaehler manifold together with a line bundle, thought of as an object in the derived category. These comprise the deformed Hermitian Yang-Mills equations of Leung-Yau-Zaslow, and specialise to the Kaehler Yang-Mills equations of Alvarez-Consul, Garcia-Fernandez and Garcia-Prada in the large radius limit. The first part of the talk will be devoted to geometric motivation, in particular through a moment map interpretation. The second part will be more analytic and will focus on abelian varieties, following ideas of Feng-Szekelyhidi.