We explain how to deduce from recent results in the Minimal Model Program a general uniruledness theorem for base loci of adjoint divisors. We also show how to recover special cases by extending a technique introduced by Takayama.Date: October 24, 2018. Key-words : big and pseff adjoints divisors; stable, non-ample and non-nef base locus; rational curves. A.M.S. classification : 14J40.
Abstract. Let X be a normal variety such that K X is Q-Cartier, and let f : X → X be a finite surjective morphism of degree at least two. We establish a close relation between the irreducible components of the locus of singularities that are not log-canonical and the dynamics of the endomorphism f . As a consequence we prove that if X is projective and f polarised, then X has at most log-canonical singularities.
We show how to use effective non-vanishing to prove that Seshadri constants of some ample divisors are bigger than 1 on smooth threefolds whose anticanonical bundle is nef or on Fano varieties of small coindice. We prove the effective non-vanishing conjecture of Ionescu-Kawamata in dimension 3 in the case of line bundles of "high" volume.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.