On the canonical bundle formula in positive characteristic

2023/05/31 by Benozzo, Marta · 1 citation
#14D06 #14E30 #14G17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.19841

Abstract

Let f: X → Z be a fibration from a normal projective variety X of dimension n onto a normal curve Z over a perfect field of characteristic p>0. Let (X, B) be a dlt pair such that the induced pair on a general fibre is log canonical. Assuming the LMMP and the existence of log resolutions in dimension ≤ n, we prove that, when K_X+B is f-nef, the moduli part is nef up to a birational map Y \dashrightarrow X. As a corollary, we prove positivity of the moduli part in the K-trivial case, i.e. when K_X+B ∼_ℚ f^*L for some ℚ-Cartier ℚ-divisor L on Z. In particular, consider a dlt pair (X, B) of dimension 3 over a perfect field of characteristic p>5 such that the induced pair on a general fibre is log canonical, then the canonical bundle formula holds unconditionally.

Cited by

• Boundedness of complements for fibered Fano threefolds in positive characteristic

Related

• On the canonical bundle formula and log abundance in positive characteristic
• On canonical bundle formula for fibrations of curves with arithmetic genus one
• Projective klt pairs with nef anti-canonical divisor
• Existence of log canonical closures
• Log abundance of the moduli b-divisors of lc-trivial fibrations