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PRODID:-//Memento EPFL//
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SUMMARY:Homological projective duality for Sym^2(P(V))
DTSTART:20151124T151500
DTEND:20151124T170000
DTSTAMP:20260407T183819Z
UID:cafe8d814e6d42cb0eaa9fa2cc27c990230864c9aaab20bcbd56a70b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Jørgen Rennemo (Imperial)\nTo a smooth\, projective variety 
 X\, we associate its derived category D(X). The question of when two varie
 ties X and Y have equivalent derived categories is an interesting one\, wi
 th the case of Calabi-Yau varieties of particular interest. A famous theor
 em 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 produce
 d an example of a pair of CY 3-folds X and Y with equivalent derived categ
 ories\, but such that X & Y are not birational\, one of only a handful of 
 such examples known.\nIn the Hosono-Takagi example\, X is a complete inter
 section of divisors in Sym^2(P^4). Kuznetsov's theory of homological proje
 ctive duality is a very useful tool for understanding derived categories o
 f 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 par
 ticular produces Hosono-Takagi's example when n = 4. I will explain this r
 esult and its proof\, which is based on a powerful general technique invol
 ving categories of matrix factorisations and variation of GIT quotients.
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STATUS:CONFIRMED
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