Upper level sets of Lelong numbers on P-2 and cubic curves

KİŞİSEL A. U. Ö., YAZICI Ö.

MATHEMATISCHE ZEITSCHRIFT, vol.300, no.3, pp.2917-2930, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 300 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s00209-021-02907-3
  • Journal Name: MATHEMATISCHE ZEITSCHRIFT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.2917-2930
  • Keywords: Positive closed currents, Lelong numbers, Cubic curves
  • Middle East Technical University Affiliated: Yes

Abstract

Let T be a positive closed current of bidimension (1, 1) with unit mass on P-2 and V-alpha(T) be the upper level sets of Lelong numbers nu(T, x) of T. For any alpha >= 1/3, we show that vertical bar V-alpha(T)\C vertical bar <= 2 for some cubic curve C.