Upper Level Sets of Lelong Numbers on Hirzebruch Surfaces

KİŞİSEL A. U. Ö., YAZICI Ö.

JOURNAL OF GEOMETRIC ANALYSIS, cilt.33, sa.8, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 8
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s12220-023-01312-y
  • Dergi Adı: JOURNAL OF GEOMETRIC ANALYSIS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Hirzebruch surfaces, Lelong numbers, Positive closed currents
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Let F-a denote the Hirzebruch surfaces and T-alpha,T-alpha '(F-a) denotes the set of positive, closed (1, 1)-currents on F-a whose cohomology class is alpha F + alpha ' H where F and H generates the Picard group of F-a. E-beta(+)(T) denotes the upper level sets of Lelong numbers v(T, x) of T is an element of T-alpha,T-alpha '(F-a). When a = 0, (F-a = P-1 x P-1), for any current T is an element of T-alpha,T-alpha '(P-1 x P-1), we show that E-(alpha+alpha ')/3(+)(T) is contained in a curve of total degree 2, possibly except 1 point. For any current T is an element of T-alpha,T-alpha '(F-a), we show that E-beta(+) (T) is contained in either in a curve of bidegree (0, 1) or in a + 1 curves of bidegree (1, 0) where beta >= (alpha + (a + 1)alpha ')/(a+2).