Cone theorem and Mori hyperbolicity

2021/02/23 by Osamu Fujino, Fujino, Osamu · 1 citation
Mathematics · #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics #Degenerate energy levels #Discrete mathematics #FOS: Mathematics #Fano plane #Geometry and complex manifolds #Locus (genetics) #Mathematics #Meromorphic and Entire Functions #Modulo #Morphism #Physics #Primary 14E30 #Pure mathematics #Secondary 32Q45

paper · pdf · doi:10.48550/arxiv.2102.11986

openalex publication_date 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We discuss the cone theorem for quasi-log schemes and the Mori hyperbolicity. In particular, we establish that the log canonical divisor of a Mori hyperbolic projective normal pair is nef if it is nef when restricted to the non-lc locus. This answers Svaldi's question completely. We also treat the uniruledness of the degenerate locus of an extremal contraction morphism for quasi-log schemes. Furthermore, we prove that every fiber of a relative quasi-log Fano scheme is rationally chain connected modulo the non-qlc locus.

Citations

• Existence of minimal models for varieties of log general type
• Semipositivity theorems for moduli problems
• Remarks on special kinds of the relative log minimal model program
• Crit�res de platitude et de projectivit�

Cited by

• Existence of flips for generalized lc pairs

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• Subadjunction for quasi-log canonical pairs and its applications
• Pull-back of quasi-log structures
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• Log canonical pairs with boundaries containing ample divisors
• Fundamental theorems for semi log canonical pairs