Semi-log canonical vs F-pure singularities

JOURNAL OF ALGEBRA

卷:349

Article

Miller, Lance Edward¹  Schwede, Karl² 

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Frobenius map;    Frobenius splitting;    F-purity;    Semi-log canonical;    Log canonical;    Inversion of adjunction;    Normalization;    Seminormal;   

DOI  :  10.1016/j.jalgebra.2011.08.035

来源: Elsevier

【 摘 要 】

If X is Frobenius split, then so is its normalization and we explore conditions which imply the converse. To do this, we recall that given an O(x)-linear map phi : F*O(x) -> O(x) it always extends to a map (phi) over bar on the normalization of X. In this paper, we study when the surjectivity of (phi) over bar implies the surjectivity of phi. While this doesn't occur generally, we show it always happens if certain tameness conditions are satisfied for the normalization map. Our result has geometric consequences including a connection between F-pure singularities and semi-log canonical singularities, and a more familiar version of the (F-)inversion of adjunction formula. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free