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Symplectic resolutions for Higgs moduli spaces

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 نشر من قبل Andrea Tirelli
 تاريخ النشر 2017
  مجال البحث
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 تأليف Andrea Tirelli




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In this paper, we study the algebraic symplectic geometry of the singular moduli spaces of Higgs bundles of degree $0$ and rank $n$ on a compact Riemann surface $X$ of genus $g$. In particular, we prove that such moduli spaces are symplectic singularities, in the sense of Beauville [Bea00], and admit a projective symplectic resolution if and only if $g=1$ or $(g, n)=(2,2)$. These results are an application of a recent paper by Bellamy and Schedler [BS16] via the so-called Isosingularity Theorem.



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