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SUMMARY:Hyperpolygons and moduli spaces of parabolic Higgs bundles - Mandi
 ni\, A (Tcnica de Lisboa)
DTSTART:20110627T130000Z
DTEND:20110627T133000Z
UID:TALK31899@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Given an $n$-tuple of positive real numbers $lpha$ we conside
 r the hyperpolygon space $X(lpha)$\, the hyperkhler quotient analogue to 
 the Khler moduli space of polygons in $mathbb{R}^3$. There exists an isomo
 rphism between hyperpolygon spaces and moduli spaces of stable\, rank-$2$\
 , holomorphically trivial parabolic Higgs bundles over $mathbb{C} mathbb{P
 }^1$ with fixed determinant and trace-free Higgs field. This allows us to 
 prove that hyperpolygon spaces $X(lpha)$ undergo an elementary transforma
 tion in the sense of Mukai as $lpha$ crosses a wall in the space of its a
 dmissible values. We describe the resulting changes in the core of $X(lph
 a)$ as well as the changes in the nilpotent cone of the corresponding modu
 li spaces of PHBs. If time permits\, we will explain how to obtain explici
 t formulas for the computation of the intersection numbers of the core com
 ponents of $X(lpha)$ and of the nilpotent cone components of the correspo
 nding moduli spaces of PHBs. As a final application\, we describe the coho
 mology ring structure of these moduli spaces of PHBs and of the components
  of their nilpotent cone. This is joint work with Leonor Godinho.\n
LOCATION:Seminar Room 1\, Newton Institute
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