On the three dimensional minimal model program in positive characteristic

By Christopher D. Hacon. 2013

165 citations recorded by the source corpus.

Let $f:(X,B)\to Z$ be a 3-fold extremal dlt flipping contraction defined over an algebraically closed field of characteristic $p>5$, such that the coefficients of $\{B\}$ are in the standard set $\{1-\frac 1n|n\in \mathbb N\}$, then the flip of $f$ exists. As a consequence, we prove the existence of minimal models for any projective $\Q$-factorial terminal variety $X$ with pseudo-effective canonical divisor $K_X$.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/391fbd804784e9a3fe8a550b827d2347b4008208

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Citations in the corpus

Existence of flips and minimal models for 3-folds in char p (2013, background): “dlt and p > 5. However, we still need contractions to algebraic spaces as an auxiliary tool. 6.2. Existence of generalized ﬂips. We recall the deﬁnition of generalized ﬂips which was introduced in [13]. Let (X,B) be a projective Q-factorial pair of dimension 3 over k char p > 0, and let R be a”
Existence of Mori fibre spaces for 3-folds in char $p$ (2014, background): “One of the fundamental ingredients of this paper is the following result which was proved after the developments in [12].”
Rational points on log Fano threefolds over a finite field (2015, background): “ may assume that ∆ is a prime divisor, in particular the pair is plt. Then, the base change (X×kk,∆×kk) to the algebraic closure is also plt. Since ∆×kkis normal by Theorem 3.1 and Proposition 4.1 in [HX15], so is ∆. Theorem 2.12 (MMP with scaling). Let kbe a perfect ﬁeld of characteristic p>5, a”
Purely Log Terminal Threefolds with Non-Normal Centres in Characteristic Two (2016, background): “For example, if X is either a surface or a threefold in characteristic p > 5, then the question holds true [HX15, Theorem 3.1 and Proposition 4.1].”
On base point freeness in positive characteristic (2013, methodology): “Theorem 4.10], we get the contraction as described in Case (2). If KX + His big, then we proceed with a step of a generalized minimal model program, given by a KX-negativemap X99K X 1 as described in [HX13], and we can replaceXby X 1. It follows from termination of generalizedﬂips (see [HX13, Sectio”
On the rationality of Kawamata log terminal singularities in positive characteristic (2017, background): “tion in positive characteristic p>0 is much more complicated. In spite of this, it is known that the klt MMP is valid in dimension two ([Tan14]) and dimension three when the characteristic p>5 ([HX15], [CTX15], [Bir16], [BW17]). It is natural to wonder if in positive characteristic, klt singul”