Theta Functions for (n) versus (n)

الأصل · EN

Over a smooth complex projective curve C of genus g let (n,d) be the moduli space of semistable bundles of rank n and degree d on C, and (n,L), the moduli space of those bundles whose determinant is isomorphic to a fixed line bundle L over C. Let θF and θ be theta bundles over these two moduli spaces. We prove a simple formula relating their spaces of sections: if h= (n,d) is the greatest common divisor of n and d, and L∈ ᵈ(C), then H⁰((n,L), θᵏ) · kᵍ= H⁰((n,d),θFᵏ)· hᵍ. We also formulate a conjectural duality between these two types of spaces of sections.