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Creators/Authors contains: "Schnell, Christian"

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  1. ; ; ; (, Épijournal de Géométrie Algébrique)
    We generalize the finiteness theorem for the locus of Hodge classes withfixed self-intersection number, due to Cattani, Deligne, and Kaplan, from Hodgeclasses to self-dual classes. The proof uses the definability of periodmappings in the o-minimal structure $$\mathbb{R}_{\mathrm{an},\exp}$$. 
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  2. ; (, Journal of the American Mathematical Society)
    null (Ed.)
    We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient condition for this, whose proof relies on the Decomposition Theorem and Saito’s theory of mixed Hodge modules. We use it to generalize the theorem of Greb-Kebekus-Kovács-Peternell to complex spaces with rational singularities, and to prove the existence of a functorial pull-back for reflexive differentials on such spaces. We also use our methods to settle the “local vanishing conjecture” proposed by Mustaţă, Olano, and Popa. 
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  3. ; ; (, Selecta Mathematica)
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  4. ; ; (, Local and global methods in algebraic geometry)
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