Talks by prof Alexander Kuznetsov

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINARS
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Professor Alexander Kuznetsov (Steklov Mathematical Institute,
Moscow) will give the following talks. Both talks will take place
in Room 136, SISSA Building A.

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Title: Geometry of Fano manifolds of degree 10
Time: Thursday, July 24th, 11:30 am

Abstract: I will talk about the work in progress with Olivier Debarre and
Olivier Benoist concerning the geometry of Fano manifolds of degree 10.
There are two types of such manifolds --- intersections of Gr(2,5) with
a quadric (and their linear sections), and double coverings of Gr(2,5)
ramified in a quadric (and their linear sections), called ordinary and
hyperelliptic respectively. I will discuss relation of these manifolds
to EPW sextics and an interesting correspondence on (the closure of)
moduli space of such manifolds relating manifolds of different type
and dimension.

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Title: Derived categories of Fano manifolds of degree 10
Time: Tuesday, July 29th, 11:30 am

Abstract: I will discuss the structure of derived categories of Fano manifolds
of degree 10. They admit a semiorthogonal decomposition with several exceptional
objects (coming from the ambient Grassmannian) and a nontrivial component,
which in the case of even dimension behaves like derived category of a K3 surface.
Conjecturally, the varieties related by the correspondence of the previous talk
have equivalent nontrivial components. I will prove this in some cases.
This is a work in progress joint with Alex Perry.

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U. Bruzzo