Manish Kumar
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Manish Kumar has a total of 9 co-authors. Here are the top co-authors by number of shared publications:
- Indranil Biswas
Department of Mathematics, Shiv Nadar University, Greater Noida, India
16 shared publications - A. J. Parameswaran
School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India
12 shared publications - A. J. Parameswaran
Kerala School of Mathematics, Kozhikode, India
5 shared publications - Umesh V. Dubey
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute, Chhatnag Road, Jhunsi, Prayagraj 211019, India
2 shared publications A. J. Parameswaran
1 shared publicationIndranil Biswas
Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida, Uttar Pradesh 201314, India
1 shared publication
Latest Publications
- Open Access
Virtual global generation in higher dimensions
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 study relationship between these notions. All these notions agree for curves but in higher dimension we show that this is not the case.
Open AccessVirtual global generation in higher dimensions
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 study relationship between these notions. All these notions agree for curves but in higher dimension we show that this is not the case.
- 27 August 2025
- Published by Springer Nature in Proceedings - Mathematical Sciences
- Vol. 135 (2) , 1-10
On the equivariant vector bundles on $\pmb {\mathbb{C}\mathbb{P}^1}$- 27 August 2025
- Published by Springer Nature in Proceedings - Mathematical Sciences
- Vol. 135 (2) , 1-10
On the equivariant vector bundles on $\pmb {\mathbb{C}\mathbb{P}^1}$- Open AccessOn the equivariant vector bundles on $\mathbb{CP}^1$Let $H$ be a subgroup of ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) such that the Zariski closure in ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) of some compact subgroup of $H$ contains $H$. We classify the $H$--equivariant holomorphic vector bundles on $\mathbb{CP}^1$. This generalizes \cite{BM} where $H$ was assumed to be a finite abelian group.Open AccessOn the equivariant vector bundles on $\mathbb{CP}^1$Let $H$ be a subgroup of ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) such that the Zariski closure in ${\rm PGL}(2,\mathbb C)$ (respectively, ${\rm SL}(2,\mathbb C)$) of some compact subgroup of $H$ contains $H$. We classify the $H$--equivariant holomorphic vector bundles on $\mathbb{CP}^1$. This generalizes \cite{BM} where $H$ was assumed to be a finite abelian group.
- Open Access
Isomorphism of étale fundamental groups lifts to isomorphism of stratified fundamental group
It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the étale fundamental groups, then the induced map of the stratified fundamental groups $π_1^{str}(f)\, :\, π_1^{str}(Y,\, y)\,\longrightarrow\, π_1^{str}(X,\, f(y))$ is also an isomorphism.Open AccessIsomorphism of étale fundamental groups lifts to isomorphism of stratified fundamental group
It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the étale fundamental groups, then the induced map of the stratified fundamental groups $π_1^{str}(f)\, :\, π_1^{str}(Y,\, y)\,\longrightarrow\, π_1^{str}(X,\, f(y))$ is also an isomorphism. - 27 March 2025
- Published by Springer Nature in Proceedings - Mathematical Sciences
- Vol. 135 (1) , 1-15
A criterion for solving embedding problems for the étale fundamental group of curves
- 27 March 2025
- Published by Springer Nature in Proceedings - Mathematical Sciences
- Vol. 135 (1) , 1-15
A criterion for solving embedding problems for the étale fundamental group of curves
- Open Access
Direct image of structure sheaf and parabolic stability
Let $f : X \rightarrow Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We prove that $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ equipped with a natural parabolic structure is parabolic polystable. Several conditions are given that ensure that the parabolic vector bundle $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ is actually parabolic stable.Open AccessDirect image of structure sheaf and parabolic stability
Let $f : X \rightarrow Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We prove that $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ equipped with a natural parabolic structure is parabolic polystable. Several conditions are given that ensure that the parabolic vector bundle $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ is actually parabolic stable. - 17 July 2024
- Published by Springer Nature in Acta Mathematica Vietnamica
- Vol. 49 (4) , 649-665
Bertini Type Results and Their Applications
- 17 July 2024
- Published by Springer Nature in Acta Mathematica Vietnamica
- Vol. 49 (4) , 649-665
Bertini Type Results and Their Applications
- Open Access
Bertini type results and their applications
We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application, it is shown that certain class of a smooth quasi-projective variety contains a smooth curve such that irreducible lisse \ell-adic sheaves on the variety with "ramification bounded by a branch data" remains irreducible when restricted to the curve.
Open AccessBertini type results and their applications
We prove Bertini type theorems and give some applications of them. The applications are in the context of Lefschetz theorem for Nori fundamental group for normal varieties as well as for geometric formal orbifolds. In another application, it is shown that certain class of a smooth quasi-projective variety contains a smooth curve such that irreducible lisse \ell-adic sheaves on the variety with "ramification bounded by a branch data" remains irreducible when restricted to the curve.
- Open Access
Characterization of genuine ramification using formal orbifolds
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 pullback of every stable bundle remains stable in the orbifold category. We also give some other characterizations of genuine ramification. This generalizes the results of [BKP1] and [BP1]. In fact, it is a positive characteristic analogue of results in [BKP2].
Open AccessCharacterization of genuine ramification using formal orbifolds
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 pullback of every stable bundle remains stable in the orbifold category. We also give some other characterizations of genuine ramification. This generalizes the results of [BKP1] and [BP1]. In fact, it is a positive characteristic analogue of results in [BKP2].
- Open Access
Pushforward of structure sheaf and virtual global generation
Let $f:X\rightarrow Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is virtually globally generated. Moreover, $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is ample if and only if $f$ is genuinely ramified.Open AccessPushforward of structure sheaf and virtual global generation
Let $f:X\rightarrow Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is virtually globally generated. Moreover, $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is ample if and only if $f$ is genuinely ramified.