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Thomas Prince

Smoothing Calabi-Yau toric hypersurfaces using the Gross-Siebert program
Monday, 14 October, 2019 - 14:00
Résumé : 

We describe how to form a novel dataset of Calabi-Yau threefolds via an application of the Gross-Siebert algorithm to a reducible union of toric varieties obtained by degenerating anti-canonical hypersurfaces in a class of (around 1.5 million) Gorenstein toric Fano fourfolds. Many of these constructions correspond to smoothing such a hypersurface; in contrast to the famous construction of Batyrev-Borisov which performs a crepant resolution. In addition we describe a possible mirror construction, which allows us to describe the Picard-Fuchs operators associated to these examples. We focus particularly on a class of examples related to joins of elliptic curves, including examples recently considered by Inoue and Knapp-Sharpe.

Institution de l'orateur : 
Thème de recherche : 
Algèbre et géométries
Salle : 
Salle 04
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