| 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 |
