Speaker
Dr
Tim Gräfnitz
Description
I explain how Fano smoothings of Gorenstein toric varieties can be constructed using logarithmic geometry. Maximally mutable Laurent polynomials induce singular log structures on reducible toroidal crossing spaces. Conjecturally, such a space admits a log crepant resolution if and only if the Laurent polynomial is rigid. For three-dimensional examples, I construct these log resolutions explicitly using sequences of blow-ups and flops. Once a log resolution has been obtained, a general smoothing theorem of Felten-Filip-Ruddat applies. The resulting construction also provides a framework for studying mirror symmetry and tropical geometry. This is joint work with Alessio Corti and Helge Ruddat.