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arXiv · 2003.02612

New singularity invariants : the sheaf $\beta_X^\bullet$

Daniel Barlet
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Abstract

The graded coherent sheaf $\alpha_X^\bullet$ constructed in [B.18] for any reduced pure dimensional complex space $X$ is stable by exterior product but not by the de Rham differential. We construct here a new graded coherent sheaf $\alpha_X^\bullet$ containing $\alpha_X^\bullet$ and stable both by exterior product and by the de Rham differential. We show that it has again the ``pull-back property'' for holomorphic maps $f : X \to Y$ between irreducible complex spaces such that $f(X)$ is not contained in the singular set of $Y$. Moreover, this graded coherent sheaf $\alpha_X^\bullet$ comes with a natural coherent exhaustive filtration and this filtration is also compatible with the pull-back by such holomorphic maps. These sheaves define new invariants on singular complex spaces. We show on some simple examples that these invariants are new.

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Daniel Barlet. 2020-03-05. New singularity invariants : the sheaf $\beta_X^\bullet$. https://arxiv.org/abs/2003.02612

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