New constructions of Fano 3-folds from mirror symmetry
- Date: Tuesday 3 March 2020, 16:00 – 17:00
- Location: Mathematics Level 8, MALL 1, School of Mathematics
- Type: Seminars, Pure Mathematics, Algebra
- Cost: Free
Liana Heuberger, Loughborough University. Part of the algebra seminar series.
Mirror symmetry conjecturally associates to a Fano orbifold a (very special type of) Laurent polynomial. Laurent inversion is a method for reversing this process, obtaining a Fano variety from a candidate Laurent polynomial. We apply this to construct previously unknown Fano 3-folds with terminal Gorenstein quotient singularities.
A Laurent polynomial f determines, through its Newton polytope P, a toric variety X_P, which is in general highly singular. Laurent inversion constructs, from f and some auxiliary data, an embedding of X_P into an ambient toric variety F. In many cases this embeds X_P as a complete intersection of line bundles on F, and the general section of these line bundles is the Q-Fano 3-fold that we seek.
This is joint work with Tom Coates, Al Kasprzyk and Giuseppe Pitton.