Given a scheme Y and a subscheme Z \subset Y we construct

a sequence of triangulated categories D_n(Z,Y), such that

D_0(Z,Y) is equivalent to the derived category of the blowup

X of Y in Z, and for n > 0 there is a semiorthogonal

decomposition D_n(Z,Y) with one component equivalent

to the derived category of X and n copies of the derived

category of Z. These categories are called the higher blowup

categories. Each higher blowup category comes with a pair of adjoint

functors \pi_*:D_n(Z,Y) \to D(Y) and \pi^*:D(Y) \to D_n(Z,Y)

(generalizing the pushforward and the pullback functors for the blowup

morphism \pi:X \to Y), and for n >> 0 the composition \pi_*\circ \pi^*

is isomorphic to identity. This is a joint work in progress with Dima Kaledin.

## SISSA GEOMETRY SEMINARS: Higher Blowups

Research Group:

Prof.

Alexander Kuznetsov

Institution:

Steklov Institute, Moscow

Location:

A-136

Schedule:

Wednesday, July 31, 2013 - 14:30 to 16:00

Abstract: