Seminar
| Parent Program: | |
|---|---|
| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Mirror Symmetry for Q-Fano 3-folds
A Q-Fano 3-fold Y is a projective variety with mild (terminal) singularities, ample anticanonical class, and Picard rank 1. As opposed to the smooth case, Q-Fano 3-folds are not classified (and these varieties appear as end-products of the 3-fold MMP). While there are only 17 deformation families of smooth Fano 3-folds with Picard rank 1, we expect thousands of deformation families of Q-Fano 3-folds. Using heuristics from the SYZ and Kontsevich’s Homological Mirror Symmetry conjectures, we will explain that the mirror of a Q-Fano 3-fold is expected to be a log Calabi-Yau pair (X,D) equipped with a map to the projective line which is a K3 fibration such that a power of the monodromy of the mirror family at infinity is maximally unipotent. In agreement with mirror symmetry predictions, we will describe explicitly the mirror of Miles Reid's 95 families of Q-Fano 3-fold hypersurfaces in weighted projective space embedded by -K_Y as special families of K3 surfaces and we will see how geometric properties of these Q-Fano 3-folds can be read from the mirror family.
No Notes/Supplements Uploaded