Séminaire Géométries ICJ

Canonical representatives of complexified Kähler classes

by Carlo Scarpa

112 (ICJ)



1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua

In this talk, we consider the problem of finding a canonical representative of a complexified Kähler class on a compact complex manifold, motivated by fundamental constructions in mirror symmetry. In 2020, Schlitzer and Stoppa proposed to fix such a representative as the solution of a system of PDEs obtained by coupling two conditions that are well-known to Kähler geometers: the deformed Hermitian Yang-Mills and constant scalar curvature equations. We will first give a general introduction to their construction, and then present a variational framework that can be used to establish uniqueness of solutions of the system on complex surfaces.