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F-adjunction · Around

2009

F-adjunction

Schwede, Karl

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In this paper we study singularities defined by the action of Frobenius in characteristic $p > 0$.

We prove results analogous to inversion of adjunction along a center of log canonicity.
For example, we show that if $X$ is a Gorenstein normal variety then to every normal center of sharp $F$-purity $W \subseteq X$ such that $X$ is $F$-pure at the generic point of $W$, there exists a canonically defined $\bQ$-divisor $\Delta_{W}$ on $W$ satisfying $(K_X)|_W \sim_{\bQ} K_{W} + \Delta_{W}$.
Furthermore, the singularities of $X$ near $W$ are "the same" as the singularities of $(W, \Delta_{W})$.

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R. Hartshorne
1966
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M. Hochster and J. L. Roberts
1976
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R. Hartshorne
1977
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R. Fedder
1983
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V. B. Mehta and A. Ramanathan
1985
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M. Hochster and C. Huneke
1987
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1987
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N. Bourbaki
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R. Fedder and K. Watanabe
1989
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M. Hochster and C. Huneke
1990
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1991
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J. Kollár and 14 coauthors
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1994
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