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SUMMARY:Carlos Florentino (Faculdade de Ciências da Universidade de Lisbo
 a)
DTSTART:20230926T150000Z
DTEND:20230926T160000Z
DTSTAMP:20260423T022723Z
UID:Geolis/128
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/128/"
 >Symplectic resolutions of moduli spaces of G-Higgs bundles over abelian v
 arieties</a>\nby Carlos Florentino (Faculdade de Ciências da Universidade
  de Lisboa) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nFollowing 
 A. Beauville\, a complex algebraic variety $X$ is said to be symplectic if
  it admits a holomorphic symplectic form $\\omega$ on its smooth locus suc
 h that\, for every resolution $\\pi: Y \\to X$\, $\\pi^*\\omega$ extends t
 o a holomorphic $2$-form on $Y$. When this extension is actually non-degen
 erate (a de facto symplectic form) on $Y$\, we call $\\pi$ a symplectic (o
 r crepant) resolution.\n\nLet $G$ be a complex reductive group and $A$ an 
 abelian variety of dimension $d$. The aim of this talk is to show that all
  moduli spaces of $G$-Higgs bundles over $A$ are symplectic varieties\, an
 d that\, for $G=\\mathrm{GL}(n\,\\mathbb C)$\, the canonical Hilbert-Chow 
 morphism is a symplectic resolution if and only if $d=1$.\n\nMoreover\, us
 ing a little representation theory\, we can obtain explicit expressions fo
 r the Poincaré polynomials of all Hilbert-Chow resolutions (either $d=1$\
 , all $n$\; or $n=1\,2\,3$ and all $d$). This is joint work with I. Biswas
  and A. Nozad.\n
LOCATION:https://researchseminars.org/talk/Geolis/128/
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