DMM (Derived category, Mirror symmetry and McKay correspondence) seminar

Speaker: Shinobu Hosono (U Tokyo)
Title: Mirror symmetry and projective geometry of Reye congruences
Date (JST): Thu, Mar 10, 2011, 10:30 - 17:00
Place: Seminar Room B
Abstract: Part I;
Non-birational Calabi-Yau manifolds, X and Y, which have an equivalent derived category are called Fourier-Mukai(FM) partner to each other. I will consider the mirror symmetry of such FM partners. To have a general picture, I will review the case of K3 surfaces based on the work with Lian, Oguiso, Yau (J.Alg.Geom.2004). After that I will introduce a well-studied example of Calabi-Yau threefold due to Rodland (and studied further in details by Borisov and Caldararu, Kuznetsov).

Part II;
Studying the mirror family in detail, I will show that the three dimensional Reye congruence X provides us a non-trivial example of FM partner of Calabi-Yau threefolds, which has similar properties to the example by Rodland. Looking into the relevant projective geometry of the Reye congruence, I will construct the (possible) FM partner Y to X as the double covering of a determinantal quintic in P4. I will also determine the BPS numbers of them using the mirror symmetry.

This talk is based on a recent work with Hiromichi Takagi, arXiv.mathAG/1101.2746.
Remarks: 10:30-11:30 Shinobu Hosono
11:45-13:00 Lunch seminar by Kentaro Hori
13:30-15:00 Shinobu Hosono
15:30-17:00 Kentaro Hori