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arXiv · 1005.5207

Base change behavior of the relative canonical sheaf related to higher dimensional moduli

Zsolt Patakfalvi
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Abstract

We show that the compatibility of the relative canonical sheaf with base change fails generally in families of normal varieties. Furthermore, it always fails if the general fiber of a family of pure dimension n is Cohen-Macaulay and the special fiber contains a strictly S_{n-1} point. In particular, in moduli spaces with functorial relative canonical sheaves Cohen-Macaulay schemes can not degenerate to S_{n-1} schemes. Another, less immediate consequence is that the canonical sheaf of an S_{n-1}, G_2 scheme of pure dimension n is not S_3.

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Zsolt Patakfalvi. 2012-02-28. Base change behavior of the relative canonical sheaf related to higher dimensional moduli. https://doi.org/10.2140/ant.10.2013.7.353

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