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

By Karl Schwede. 2011

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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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bc9d3bb1859d88aa0f1db71429fa5f9cbeba237b

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Citations in the corpus

The Waldschmidt constant for squarefree monomial ideals (2015, background): “, in number theory [5, 28, 29], complex analysis [26], algebraic geometry [3, 4, 11, 24] and commutative algebra [18].”
On the three dimensional minimal model program in positive characteristic (2013, background): “Here Treg is defined by the pushing forward via f∗ of the sequence F eg∗ OX((1− peg)(KX +Δ) + pegM) → F eg∗ OX((1− peg)KX + pegM) → OX(M), which is obtained tensoring the sequence in [Schwede11, Section 2] by OX(M).”
Asymptotic resurgences for ideals of positive dimensional subschemes of projective space (2012, background): “It is often challenging just to find good lower bounds for γ(I); see [9, 13, 21].”