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