469 research outputs found

    Weak positivity via mixed Hodge modules

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    We prove that the lowest nonzero piece in the Hodge filtration of a mixed Hodge module is always weakly positive in the sense of Viehweg.Comment: 9 page

    On a theorem of Campana and P\u{a}un

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    Let XX be a smooth projective variety over the complex numbers, and ΔX\Delta \subseteq X a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and P\u{a}un: If some tensor power of the bundle ΩX1(logΔ)\Omega_X^1(\log \Delta) contains a subsheaf with big determinant, then (X,Δ)(X, \Delta) is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.Comment: 9 pages. Formatted using epigamath.st
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