Supplements to non-lc ideal sheaves

Abstract

We consider various definitions of non-lc ideal sheaves -- generalizations of the multiplier ideal sheaf which define the non-lc (non-log canonical) locus. We introduce the maximal non-lc ideal sheaf and intermediate non-lc ideal sheaves and consider the restriction theorem for these ideal sheaves. We also begin the development of the theory of a characteristic p>0 analog of maximal non-lc ideals, utilizing some recent work of Blickle.

46 pages, v2: the definition of the ideal $σ((R, Δ), \ba^t)$ (Definition 14.4) slightly changed, typos corrected, to appear in RIMS Kokyuroku Bessatsu

References in corpus (5)

• F-thresholds and Bernstein-Sato polynomials
• Introduction to the log minimal model program for log canonical pairs
• Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities
• Test ideals via algebras of $p^{-e}$-linear maps
• Fundamental theorems for the log minimal model program

Cited by in corpus (3)

• Test ideals in rings with finitely generated anti-canonical algebras
• Introduction to the theory of quasi-log varieties
• On the three dimensional minimal model program in positive characteristic