Boundedness of $(\epsilon ,n)$-Complements for Surfaces

Abstract

We show the existence of $(\epsilon ,n)$-complements for $(\epsilon ,\mathbb{R})$-complementary surface pairs when the coefficients of boundaries belong to a DCC set.

69 pages. Fixed some typos. Dedicated to Vyacheslav Shokurov on the occasion of his seventieth birthday

References in corpus (9)

• ACC for minimal log discrepancies of exceptional singularities
• Birational boundedness of rationally connected Calabi-Yau 3-folds
• Log Calabi-Yau fibrations
• Toward the equivalence of the ACC for $a$-log canonical thresholds and the ACC for minimal log discrepancies
• Existence and boundedness of $n$-complements
• Log canonical $3$-fold complements
• Complements on log canonical Fano varieties
• Some Results about the Index Conjecture for log Calabi-Yau Pairs
• ACC for log canonical threshold polytopes

Cited by in corpus (3)

• Shokurov's conjecture on conic bundles with canonical singularities
• An optimal gap of minimal log discrepancies of threefold non-canonical singularities
• Boundedness of ($\epsilon ,n$)-Complements for projective generalized pairs of Fano type