The geometry of Ulrich bundles on del Pezzo surfaces
JOURNAL OF ALGEBRA, cilt.375, ss.280-301, 2013 (SCI-Expanded, Scopus)
- 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.