SISSA algebraic geometry online seminars - Hayato MORIMURA

Alessandro Nobile anobile at
Tue Nov 3 10:02:06 CET 2020

Dear all,
    this is to announce the second seminar of the group of algebraic
geometry in SISSA. 


TITLE:      Categorical generic fiber 

WHEN:       Thursday, November 5 at 4.30pm (Rome) 

WHERE:      Link Zoom:
            ID riunione:  851 5174 7994
            Passcode:     604851

ABSTRACT:   For smooth separated families over a noetherian regular
affine scheme, we give an alternative description of the derived
category of the generic fiber as a Verdier quotient. When the family is
a proper effectivization of a formal deformation, the Verdier quotient
is equivalent to the derived category of the general fiber introduced by
Huybrechts--Macrì--Stellari. We also study the induced Fourier--Mukai
transform on the generic fiber. If either of those families is locally
projective, then general fibers are derived-equivalent if and only if so
are the generic fiber. As an application, given a pair of
derived-equivalent Calabi--Yau manifolds of dimension more than two, we
show that the derived equivalence can be extended to the generic fiber
of versal deformations. In this talk, after reviewing basic properties
of Serre and Verdier quotients, we explain the key idea in the proof,
which is inspired by Bondal--Van den Bergh (presumably in turn Neeman).

Everyone interested is welcomed to attend.

Best regards,

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