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no code implementations • 11 Mar 2021 • Indranil Biswas, Peter O'Sullivan

Let H be a complex Lie group acting holomorphically on a complex analytic space X such that every H-invariant regular function on X_{red} is constant.

Algebraic Geometry Category Theory 32L10, 53C55, 14D21, 16B50

no code implementations • 5 Mar 2021 • Indranil Biswas, Swarnava Mukhopadhyay, Richard Wentworth

For a simple, simply connected, complex group G, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points.

Algebraic Geometry High Energy Physics - Theory Differential Geometry Representation Theory Primary: 14H60, 32G34, 53D50, Secondary: 81T40, 14F08

no code implementations • 17 Feb 2021 • Indranil Biswas, A. J. Parameswaran

Let $f:C\rightarrow D$ be a nonconstant separable morphism between irreducible smooth projective curves defined over an algebraically closed field.

Algebraic Geometry 14H30, 14H60, 14E20

no code implementations • 26 Jan 2021 • Indranil Biswas, Mahan Mj

We prove that any one-relator group $G$ is the fundamental group of a compact Sasakian manifold if and only if $G$ is either finite cyclic or isomorphic to the fundamental group of a compact Riemann surface of genus g > 0 with at most one orbifold point of order $n \geq 1$.

Algebraic Geometry Differential Geometry Geometric Topology

no code implementations • 8 Jan 2021 • Indranil Biswas, Steven Bradlow, Sorin Dumitrescu, Sebastian Heller

We also give a family of Higgs bundles on $\Sigma$ parametrized by a nonempty open subset of $H^0(\Sigma,\, K_\Sigma^{\otimes 2}\otimes{\mathcal O}_\Sigma(-2D))$ that correspond to conical metrics of the above type on moving Riemann surfaces.

Differential Geometry Algebraic Geometry

no code implementations • 15 Dec 2020 • Indranil Biswas, Saikat Chatterjee, Praphulla Koushik, Frank Neumann

We construct and study general connections on Lie groupoids and differentiable stacks as well as on principal bundles over them using Atiyah sequences associated to transversal tangential distributions.

Differential Geometry Category Theory Primary 53C08, Secondary 22A22, 58H05, 53D50

no code implementations • 15 Dec 2020 • Indranil Biswas, Saikat Chatterjee, Praphulla Koushik, Frank Neumann

Let $\mathbb{X}=[X_1\rightrightarrows X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mathcal{H} \subset T X_1$ transversal to the fibers of the source map.

Differential Geometry Category Theory Primary 53C08, Secondary 22A22, 58H05, 53D50

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