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Base Change Behavior of the Relative Canonical Sheaf Related to Higher Dimensional Moduli by Patakfalvi, Zsolt is a scholarly article available to read on EtoBox.

What is Base Change Behavior of the Relative Canonical Sheaf Related to Higher Dimensional Moduli about?

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.

Author

Patakfalvi, Zsolt

Published

2010

Language

EN