SISSA Geometry Seminars

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINARS
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Dr. Peter Dalakov (Bulgarian Academy of Sciences, Sofia)
will give a talk on 

Generalised G_2 Hitchin systems, cubics and special Kaehler geometry

on Tuesday, July 5th, at 4 pm in Room 136, SISSA Building A.

Abstract: The base of the Hitchin integralble system for the exceptional group G_2 has a non-trivial involution L. As shown by Hitchin and Donagi-Pantev, for a sufficiently generic point b on the base, the Hitchin fibres over b and L(b) are dual abelian varieties. The involution L also preserves some of the special Kaehler data on the base. I will discuss some work in progress (with U. Bruzzo) on extending these results to the case of the generalised (ramified) Hitchin system.

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Dr. Oleksandr Iena (University of Luxemburg) 
will give a talk on

On 1-dimensional planar sheaves: modifying Simpson moduli spaces by vector bundles

on Thursday, July 7th, at 4 pm in Room 136, SISSA Building A.

Abstract:

Fix a linear polynomial P(m)= dm+c with integer coefficients and consider the Simpson moduli space M of semistable sheaves with this Hilbert polynomial on the projective plane. A generic sheaf in M is a line bundle on its Fitting support, which is a planar projective curve of degree d.

In the talk we will discuss the following results.

1) For  Hilbert polynomials dm-1, d>3, the closed subvariety M' of sheaves that are not vector bundles on their support is a singular variety of codimension 2 in M.

2) (An open dense subset of) the exceptional divisor of the blow-up of M along M' can be naturally seen as a space of vector bundles on curves.