Séminaire Géométries ICJ

Mirror symmetry and automorphisms

by Elena kalashnikov

112 (ICJ)



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

In this talk, I will discuss joint work with Chiodo and Veniani investigating the mirror symmetry of Calabi-Yau hypersurfaces in weighted projective spaces. I will show how given such a hypersurface endowed with a finite order automorphism of a specific type, the traditional cohomological mirror statement can be both specialised and broadened to take into account the weights of the action of the automorphism and the cohomology of its fixed locus. The main tool is Berglund-Hubsch-Krawitz duality. When the automorphism is an involution, this allows us to construct generalisations of Borcea--Voisin orbifolds in any dimension and with any number of factors. For odd prime order automorphisms and dimension 2 orbifolds, this implies mirror symmetry for the associated lattice polarised K3 surfaces.