Projective Poincaré and Picard bundles for moduli spaces of vector bundles over nodal curves

2020/07/06 by C. Arusha, Arusha, C., Usha N. Bhosle +3
Mathematics · #14H60 (14J60) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2007.02535

openalex publication_date 2020/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let U^'s_L(n,d) be the moduli space of stable vector bundles of rank n with determinant L where L is a fixed line bundle of degree d over a nodal curve Y. We prove that the projective Poincare bundle on Y × U^'s_L(n,d) and the projective Picard bundle on U^'s_L(n,d) are stable for suitable polarisation. For a nonsingular point x ∈ Y, we show that the restriction of the projective Poincare bundle to x × U^'s_L(n,d) is stable for any polarisation. We prove that for arithmetic genus g≥ 3 and for g=n=2, d odd, the Picard group of the moduli space U'_L(n,d) of semistable vector bundles of rank n with determinant L of degree d is isomorphic to ℤ.

Related

• Poincaré bundle for the fixed determinant moduli space on a nodal curve
• Stability of the Poincaré bundle
• Stability of the Poincaré bundle
• On Poincare bundles of vector bundles on curves
• Restriction of the Poincaré bundle to a Calabi-Yau hypersurface