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Degeneration of spectral sequences and complex Lagrangian submanifolds

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arxiv 1907.04742 v2 pith:H3FCY65G submitted 2019-07-10 math.AG math.QAmath.RT

Borislav Mladenov This is my paper · ORCID
classification math.AGmath.QAmath.RT
keywords mathrmdegenerationlagrangianmathscrspectralahlercomplexgeneralisations
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abstract

There is a local-to-global $\mathrm{Ext}$ spectral sequence $\mathrm{E}_2^{p,q} = \mathrm{H}^p(\mathrm{L}, \Omega^q_\mathrm{L}) \Rightarrow \mathrm{Ext}^{p+q}(i_*\mathscr{O}_\mathrm{L}, i_*\mathscr{O}_{\mathrm{L}})$ for a smooth Lagrangian subvariety in a hyperk\"ahler variety. We prove its degeneration on $\mathrm{E}_{2}$, and various generalisations thereof.

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    math.AG 2024-11 conditional novelty 7.0 of 10

    A moduli-space construction realizes the Laza-Saccà-Voisin compactification and yields infinitely many new families of O'Grady's ten-dimensional hyper-Kähler manifolds.

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