The Determinant Bundle on the Moduli Space of Stable Triples over a Curve

Proceedings Mathematical Sciences

N Raghavendra¹  Indranil Biswas² 

[1] Advanced Technology Centre, Tata Consultancy Services, K.L.K. Estate, Fateh Maidan Road, Hyderabad 00 00, India$$;School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 00 00, India$$

关键词: Moduli space;    stable triples;    determinant bundle;    Quillen metric.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We construct a holomorphic Hermitian line bundle over the moduli space of stable triples of the form (𝐸1, 𝐸2, 𝜙), where 𝐸1 and 𝐸2 are holomorphic vector bundles over a fixed compact Riemann surface 𝑋, and 𝜙 : 𝐸2 → 𝐸1 is a holomorphic vector bundle homomorphism. The curvature of the Chern connection of this holomorphic Hermitian line bundle is computed. The curvature is shown to coincide with a constant scalar multiple of the natural Kähler form on the moduli space. The construction is based on a result of Quillen on the determinant line bundle over the space of Dolbeault operators on a fixed 𝐶∞ Hermitian vector bundle over a compact Riemann surface.

【 授权许可】

Unknown