Indranil Biswas

Monodromy of stratified vector bundles

Indranil Biswas, Manish Kumar, A. J. Parameswaran

We explore the interconnections between the monodromy group of stratified bundles on a smooth projective variety $X$ and the monodromy of the strongly semistable vector bundles $V$ …

On the Harder-Narasimhan filtration of the direct image of the structure sheaf

Indranil Biswas, Manish Kumar, A. J. Parameswaran

We compute the Harder-Narasimhan filtration of vector bundles $f_{*} O_{Y}$ for certain finite morphisms $f : Y ⟶ X$ and in some other cases.

Normal Functions, Even Theta Characteristics and the Theta Divisor

Indranil Biswas, Lorenzo Fassina, Gian Pietro Pirola

Let $[C]$ be a general point in the moduli space of curves $M_{g}$ with $g > 1$ . Let $G \subset J (C)$ be a connected compact subgroup of real dimension $1$ of the Jacobian, and let $…

On the triviality of direct image of coherent sheaves

Indranil Biswas, Jagadish Pine

Let $π : X ⟶ Y$ be a finite morphism of projective varieties defined over an algebraically closed field of characteristic zero. We study the necessary and suff…

Virtual global generation in higher dimensions

Indranil Biswas, Manish Kumar, A. J. Parameswaran

The notion of virtual global generation (VGG) for a vector bundle has multiple possible generalization from the case of curves to higher dimensional normal projective varieties. We…

Connections and Higgs bundles on curves defined over a number field

Indranil Biswas, Sudarshan Gurjar

Let $X_{0}$ be an irreducible smooth projective curve defined over $Q$ and $E$ a vector bundle on $X_{0}$ . We give a criterion for connections on the base ch…

Brauer group of moduli stack of parabolic $PSp (r, C)$ --bundles over a curve

Indranil Biswas, Sujoy Chakraborty, Arijit Dey

Take an irreducible smooth complex projective curve $X$ of genus $g$ , with $g \geq 3$ . Let $r$ be an even positive integer. We prove that the Brauer group of the moduli stack of…

On semi-finite vector bundles with connection over Kahler manifolds

Sanjay Amrutiya, Indranil Biswas

Let $X$ be a compact connected Kähler manifold. We consider the category $C^{EC} (X)$ of flat holomorphic connections $(E, \nabla^{E})$ over $X$ satisfying the cond…

Torsors over moduli spaces of vector bundles over curves of fixed determinant

Indranil Biswas, Jacques Hurtubise

Let $M$ be a moduli space of stable vector bundles of rank $r$ and determinant $ξ$ on a compact Riemann surface $X$ . Fix a semistable holomorphic vector bundle $F$ on $X…

On the equivariant vector bundles on $CP^{1}$

Indranil Biswas, Manish Kumar, A. J. Parameswaran

Let $H$ be a subgroup of $PGL (2, C)$ (respectively, $SL (2, C)$ ) such that the Zariski closure in $PGL (2, C)$ (respectively, ${\rm SL}(2,\math…

Isomorphism of étale fundamental groups lifts to isomorphism of stratified fundamental group

Indranil Biswas, Manish Kumar, A. J. Parameswaran

It is shown that if a finite generically smooth morphism $f : Y ⟶ X$ of smooth projective varieties induces an isomorphism of the étale fundamental groups, then…

math.CV2025

The Hexablock: a domain associated with the $μ$ -synthesis in $M_{2} (C)$

Indranil Biswas, Sourav Pal, Nitin Tomar

We introduce a domain named \textit{hexablock} in $C^{4}$ and show that its origin is a special case of $μ$ -synthesis in $M_{2} (C)$ , more precisely the $μ_{E}$ -unit ball…

A Belyi-type criterion for vector bundles on curves defined over a number field

Indranil Biswas, Sudarshan Gurjar

Let $X_{0}$ be an irreducible smooth projective curve defined over $Q$ and $f_{0} : X_{0} \to P_{Q}^{1}$ a nonconstant morphism whose…

Some recent results on the punctual Quot schemes

Indranil Biswas, Chandranandan Gangopadhyay, Ronnie Sebastian

Let $C$ be a smooth projective curve defined over the field of complex numbers. Let $E$ be a vector bundle on $C$ , and fix an integer $d ⩾ 1$ . Let $\mc Q:={\rm Quot}(E,d)$ b…

Direct image of structure sheaf and parabolic stability

Indranil Biswas, Manish Kumar, A. J. Parameswaran

Let $f : X \to Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \t…

math-ph2024

Quot scheme and deformation quantization

Indranil Biswas

Let $X$ be a compact connected Riemann surface, and let $Q (r, d)$ denote the quot scheme parametrizing the torsion quotients of $O_{X}^{\oplus r}$ of degree $d$ .…

Stability of the Parabolic Picard Sheaf

C. Arusha, Indranil Biswas

Let $X$ be a smooth irreducible complex projective curve of genus $g \geq 2$ , and let $D = x_{1} + \dots + x_{r}$ be a reduced effective divisor on $X$ . Denote by $U_{α} (L)$ the moduli…

Torsors on moduli spaces of principal $G$ -bundles

Indranil Biswas, Swarnava Mukhopadhyay

Let $G$ be a semisimple complex algebraic group with a simple Lie algebra $g$ , and let $M_{G}^{0}$ denote the moduli stack of topologically trivial stable $G$ -bu…

Characterization of genuine ramification using formal orbifolds

Indranil Biswas, Manish Kumar, A. J. Parameswaran

We give a characterization of genuinely ramified maps of formal orbifolds in the Tannakian framework. In particular we show that a morphism is genuinely ramified if and only if the…

Pushforward of structure sheaf and virtual global generation

Indranil Biswas, Manish Kumar, A. J. Parameswaran

Let $f : X \to Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that t…

Genuinely ramified maps and monodromy

Indranil Biswas, Manish Kumar, A. J. Parameswaran

For any genuinely ramified morphism $f : Y ⟶ X$ between irreducible smooth projective curves we prove that $(Y \times_{X} Y) ∖ Δ$ is connected…

Effective cone of a Grassmann bundle over a curve defined over $F_{p}$

Indranil Biswas, Shripad M. Garge, Krishna Hanumanthu

Let $X$ be an irreducible smooth projective curve defined over $F_{p}$ and $E$ a vector bundle on $X$ of rank at least two. For any $1\, \leq\, r\, <\, {\rm rank}(…