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Local uniqueness of approximations and finite determinacy of log morphisms

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arxiv 1812.02195 v2 pith:5T34ZBEH submitted 2018-12-05 math.AG math.AC

Helge Ruddat This is my paper · ORCID
classification math.AGmath.AC
keywords determinacyfinitefibreslocalmorphismsapplicationapproximationscycles
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I prove a local finite determinacy result of singular fibres in families. As an application, I generalize finite determinacy results on the fibres of log morphisms and nearby and vanishing cycles sheaves by Illusie and Kisin.

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  1. Smoothing toroidal crossing spaces

    math.AG 2019-08 conditional novelty 8.0 of 10

    A proof that toroidal crossing spaces with a simple logarithmic section and a transverse anticanonical divisor admit smoothings, together with a proof of Danilov's Hodge-de Rham degeneration conjecture.

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