Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Affine geometry of three-solvmanifolds and SYZ non-Kaehler Mirror Symmetry

Alessandro Vannini

created by daniele on 14 Feb 2023
modified on 06 Mar 2023

12 apr 2023 -- 11:30

Aula Tricerri, DIMaI, Firenze

Seminari di Geometria del Dini

Abstract.

We present examples of pairs of six-dimensional compact manifolds satisfying a non-Kaehler version of Mirror Symmetry as formulated by Lau-Tseng-Yau using SU(3)-structures. In this new setting, the Calabi-Yau geometry is replaced by the symplectic half-flat geometry on the IIA-side and by the complex-balanced geometry on the IIB-side. The link between the two is provided by the Strominger-Yau-Zaslow construction which relies on the presence of a third space B over which the IIA-side fibers in Lagrangian tori. We will show how to build these examples using the theory of solvmanifolds and how it is linked to the affine geometry of the base of the fibration. Finally we will describe the action of the Fourier-Mukai transform on semi-flat differential forms and how it realizes the equivalence of the Tseng-Yau cohomology on the IIA-side with the Bott-Chern cohomology on the IIB-side. This is a joint work with L. Bedulli.

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