Geometry Seminar at Sissa

[Ugo Bruzzo]

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SISSA GEOMETRY SEMINARS
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Daniele Faenzi (Universita' di Firenze)

Homogeneous instanton bundles on P3 for an action of SL(2)

Friday, October 27, 2:30 pm room C (basement, SISSA main building)

Abstract: A k-instanton on the complex projective 3-space is a stable 
holomorphic vector
bundle of rank 2, with trivial determinant, c_2 =k, and satisfying
H^1(E(-2))=0.
Once fixed a faithful linear action of SL(2) on P3, we ask which 
k-instantons
are fixed by all the isometries of SL(2), namely, which k-instantons are
SL(2)-homogeneous. Among these are the so-called special instantons.
We will show that, besides this class of examples, there is only one 
more action
of SL(2) admitting homogeneous instantons. These turn out to be 
isolated and
admit a very simple minimal resolution, while k must be of the form
a(a+1)/2.

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Claudio Fontanari (Politecnico di Torino)

The Kodaira dimension of the moduli space of curves and the Slope 
Conjecture

Friday, October 27, 4:00 pm room C (basement, SISSA main building)