Equivariant principal bundles and logarithmic connections on toric varieties

2015/07/09 by Indranil Biswas, Biswas, Indranil, Arijit Dey +3
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14L30 #14M17 #14M27 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #math.AG #msc:14L30 #msc:14M17 #msc:14M27

paper · pdf · doi:10.48550/arxiv.1507.02415

arxiv created 2015/07/09 · openalex publication_date 2015/07/09 · arxiv updated 2015/07/10 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let M be a smooth complex projective toric variety equipped with an action of a torus T, such that the complement D of the open T--orbit in M is a simple normal crossing divisor. Let G be a complex reductive affine algebraic group. We prove that an algebraic principal G--bundle E_G→ M admits a T--equivariant structure if and only if E_G admits a logarithmic connection singular over D. If E_H→ M is a T-equivariant algebraic principal H--bundle, where H is any complex affine algebraic group, then E_H in fact has a canonical integrable logarithmic connection singular over D.

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