The geometry of Ulrich bundles on del Pezzo surfaces

Coskun E., Kulkarni R. S., MUSTOPA Y.

JOURNAL OF ALGEBRA, cilt.375, ss.280-301, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 375
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.jalgebra.2012.08.032
  • Dergi Adı: JOURNAL OF ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.280-301
  • Anahtar Kelimeler: Ulrich bundles, Algebraic surfaces, MINIMAL RESOLUTION CONJECTURE, POINTS, BINARY
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

Given a smooth del Pezzo surface X-d subset of P-d of degree d, we isolate the essential geometric obstruction to a vector bundle on X-d being an Ulrich bundle by showing that an irreducible curve D of degree dr on X-d represents the first Chern class of a rank-r Ulrich bundle on X-d if and only if the kernel bundle of the general. smooth element of vertical bar D vertical bar admits a generalized theta-divisor. Moreover, we show that any smooth arithmetically Gorenstein surface whose Ulrich bundles admit such a characterization is necessarily del Pezzo.