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- W3204683756 abstract "Abstract Let C be a smooth projective curve of genus $2$ . Following a method by O’Grady, we construct a semismall desingularisation $tilde {mathcal {M}}_{Dol}^G$ of the moduli space $mathcal {M}_{Dol}^G$ of semistable G -Higgs bundles of degree 0 for $G=mathrm {GL}(2,mathbb {C}), mathrm {SL}(2,mathbb {C})$ . By the decomposition theorem of Beilinson, Bernstein and Deligne, one can write the cohomology of $tilde {mathcal {M}}_{Dol}^G$ as a direct sum of the intersection cohomology of $mathcal {M}_{Dol}^G$ plus other summands supported on the singular locus. We use this splitting to compute the intersection cohomology of $mathcal {M}_{Dol}^G$ and prove that the mixed Hodge structure on it is pure, in analogy with what happens to ordinary cohomology in the smooth case of coprime rank and degree." @default.
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- W3204683756 date "2021-08-02" @default.
- W3204683756 modified "2023-09-30" @default.
- W3204683756 title "INTERSECTION COHOMOLOGY OF THE MODULI SPACE OF HIGGS BUNDLES ON A GENUS 2 CURVE" @default.
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- W3204683756 doi "https://doi.org/10.1017/s1474748021000347" @default.
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