Chudnovsky's conjecture for very general points in PkN

JOURNAL OF ALGEBRA

卷:498

Article

Fouli, Louiza¹  Mantero, Paolo²  Xie, Yu³ 

[1] New Mexico State Univ, Dept Math Sci, Las Cruces, NM 88003 USA

[2] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA

[3] Widener Univ, Dept Math, Chester, PA 19013 USA

关键词: Chudnovsky's conjecture;    Initial degrees;    Symbolic powers;    Fat points;    Seshadri constant;   

DOI  :  10.1016/j.jalgebra.2017.11.002

来源: Elsevier

【 摘 要 】

We prove a long-standing conjecture of Chudnovsky for very general and generic points in P-k(N), where k is an algebraically closed field of characteristic zero, and for any finite set of points lying on a quadric, without any assumptions on k. We also prove that for any homogeneous ideal I in the homogeneous coordinate ring R = k[x(0),..., x(N)], Chudnovsky's conjecture holds for large enough symbolic powers of I. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free