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arXiv · 1107.3833

A canonical linear system associated to adjoint divisors in characteristic $p > 0$

Karl Schwede
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Abstract

Suppose that $X$ is a projective variety over an algebraically closed field of characteristic $p > 0$. Further suppose that $L$ is an ample (or more generally in some sense positive) divisor. We study a natural linear system in $|K_X + L|$. We further generalize this to incorporate a boundary divisor $\Delta$. We show that these subsystems behave like the global sections associated to multiplier ideals, $H^0(X, \mJ(X, \Delta) \tensor L)$ in characteristic zero. In particular, we show that these systems are in many cases base-point-free. While the original proof utilized Kawamata-Viehweg vanishing and variants of multiplier ideals, our proof uses test ideals.

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Karl Schwede. 2011-07-19. A canonical linear system associated to adjoint divisors in characteristic $p > 0$. https://arxiv.org/abs/1107.3833

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