On relative rational chain connectedness of threefolds with anti-big canonical divisors in positive characteristics

Yuan Wang

Vol. 290 (2017), No. 1, 231–245

DOI: 10.2140/pjm.2017.290.231

Abstract

Let $X$ be a projective klt threefold over an algebraically closed field of positive characteristic, and $f:X\to Y$ a morphism from $X$ to a projective variety $Y$ of dimension $1$ or $2$. We study how bigness and relative bigness of $-K_X$ influences the rational chain connectedness of $X$ and fibers of $f$, respectively. We construct a canonical bundle formula and use it as well as the minimal model program to prove two results in this context.

Keywords

rational chain connectedness, positive characteristic, minimal model program, weak positivity, canonical bundle formula

Mathematical Subject Classification 2010

Primary: 14M22

Secondary: 14E30

Milestones

Received: 25 January 2016

Revised: 23 November 2016

Accepted: 31 January 2017

Published: 7 July 2017