Nonabelian theta functions of positive genus
Proceedings of the American Mathematical Society, cilt.136, sa.12, ss.4201-4209, 2008 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 136 Sayı: 12
- Basım Tarihi: 2008
- Doi Numarası: 10.1090/s0002-9939-08-09467-7
- Dergi Adı: Proceedings of the American Mathematical Society
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.4201-4209
- Anahtar Kelimeler: Factorization rules, Fusion product, Parabolic vector bundles, PRV, Saturation conjecture, Theta functions
- Boğaziçi Üniversitesi Adresli: Evet
Özet
Let Cg be a smooth projective irreducible curve over ℂ of genus g ≥ 1 and let {p1, ⋯ , ps} be a set of distinct points on Cg. We fix a nonnegative integer ℓ and denote by M g(p, λ) the moduli space of parabolic semistable vector bundles of rank r on Cg with trivial determinant and fixed parabolic structure of type λ = (λ1, ⋯ , λs) at p = (p1, ⋯ , ps), where each weight λi is in Pλ(SL(r)). On Mg(p, λ) there is a canonical line bundle L(λ ℓ), whose global sections are called generalized parabolic SL(r)-theta functions of order ℓ. In this paper we prove the existence of such nonzero nonabelian theta functions, thus establishing a part of higher genus generalizations of the celebrated saturation conjectures. © 2008 American Mathematical Society.