Homological projective duality for Sym^2(P(V))
Event details
| Date | 24.11.2015 |
| Hour | 15:15 › 17:00 |
| Speaker | Jørgen Rennemo (Imperial) |
| Location | |
| Category | Conferences - Seminars |
To a smooth, projective variety X, we associate its derived category D(X). The question of when two varieties X and Y have equivalent derived categories is an interesting one, with the case of Calabi-Yau varieties of particular interest. A famous theorem of Bridgeland says that if X and Y are birational Calabi-Yau 3-folds, then D(X) is equivalent to D(Y). A few years ago Hosono and Takagi produced an example of a pair of CY 3-folds X and Y with equivalent derived categories, but such that X & Y are not birational, one of only a handful of such examples known.
In the Hosono-Takagi example, X is a complete intersection of divisors in Sym^2(P^4). Kuznetsov's theory of homological projective duality is a very useful tool for understanding derived categories of such complete intersections. With Hosono-Takagi's example as motivation, we compute a "homological projective dual" of Sym^2(P^n) for any n. This allows us to understand complete intersections in Sym^2(P^n), and in particular produces Hosono-Takagi's example when n = 4. I will explain this result and its proof, which is based on a powerful general technique involving categories of matrix factorisations and variation of GIT quotients.
In the Hosono-Takagi example, X is a complete intersection of divisors in Sym^2(P^4). Kuznetsov's theory of homological projective duality is a very useful tool for understanding derived categories of such complete intersections. With Hosono-Takagi's example as motivation, we compute a "homological projective dual" of Sym^2(P^n) for any n. This allows us to understand complete intersections in Sym^2(P^n), and in particular produces Hosono-Takagi's example when n = 4. I will explain this result and its proof, which is based on a powerful general technique involving categories of matrix factorisations and variation of GIT quotients.
Practical information
- Informed public
- Free