Manish Kumar
Statistics and Mathematics Unit,
Indian Statistical Institute, Bangalore Center
Office: S2
8th Mile Mysore Road
RVCE Post, Jnana Bharti
Bangalore - 560059, India
Email: manish at isibang dot ac dot in
Phone: +91-80-26985442; +91(0)80-2848 3002 (Extn 442)


Research interests

Algebraic Geometry, Commutative algebra, Arithmetic Algebraic Geometry.

Teaching

Seminars

Publications

  1. Virtual global generation in higher dimensions (with Indranil Biswas and A. J. Parameswaran) to appear in JRMS arxiv page

  2. On equivariant vector bundles on $\mathbb{CP}^1$ (with Indranil Biswas and A. J. Parameswaran) to appear in PMSC arxiv page

  3. Isomorphism of 'etale fundamental groups lifts to isomorphism of stratified fundamental group (with Indranil Biswas and A. J. Parameswaran) to appear in IMRN arxiv page

  4. Direct image of structure sheaf and parabolic stability. (with Indranil Biswas and A. J. Parameswaran) to appear in J. Math. Sci. Univ. Tokyo arxiv page

  5. Ramified covering maps of singular curves and stability of pulled back bundles (with Indranil Biswas and A. J. Parameswaran) Rend. Circ. Mat. Palermo (2) 73 (2024), no. 4, 1555-1565. arxiv page

  6. Genuinely ramified maps and monodromy (with Indranil Biswas and A. J. Parameswaran) J. Algebra 644 (2024), 222-231. arxiv page

  7. Pushforward of structure sheaf and virtual global generation. (with Indranil Biswas and A. J. Parameswaran) Proc. Edinb. Math. Soc. (2) 67 (2024), no. 3, 663-673 arxiv page

  8. Characterization of genuine ramification using formal orbifolds (with Indranil Biswas and A. J. Parameswaran) Ark. Mat. 62 (2024), no. 2, 369-385. arxiv page

  9. A criterion for solving embedding problems for the etale fundamental group of curves (with Poulami Mandal) Proc. Indian Acad. Sci. Math. Sci. 135 (2025), no. 1, Paper No. 8, 15 pp. arxiv page

  10. Quot schemes and Fourier-Mukai transformation (with Indranil Biswas, Umesh Dubey and A. J. Parameswaran) Complex Manifolds10(2023), no.1, Paper No. 20230152, 8 pp. arxiv page

  11. The tame Nori fundamental group. (with Indranil Biswas and A. J. Parameswaran) to appear in Journal of algebra arxiv page

  12. On the stability of pulled back parabolic vector bundles (with Indranil Biswas and A. J. Parameswaran) J. Math. Sci. Univ. Tokyo 29 (2022), no. 3, 359-382. arxiv page

  13. Genuinely ramified maps and stability of pulled-back parabolic bundles (with Indranil Biswas and A. J. Parameswaran) Indag. Math. (N.S.) 33 (2022), no. 5, 956-964. arxiv page

  14. Bertini type results and their applications. (with Indranil Biswas and A. J. Parameswaran) Acta Math. Vietnam. 49 (2024), no. 4, 649-665. arxiv page

  15. Higher dimensional formal orbifolds and orbifold bundles in positive characteristic (with Indranil Biswas and A. J. Parameswaran) Comm. Algebra 50 (2022), no. 1, 300-307. arxiv page

  16. On Inertia Conjecture for Alternating group Covers (with Soumyadip Das) J. Pure Appl. Algebra 224 (2020), no. 9, 106363, 14 pp. arxiv page

  17. Ramification theory and formal orbifolds in arbitrary dimension. Proc. Indian Acad. Sci. Math. Sci. 129 (2019), no. 3, Art. 38, 34 pp. pdf-file

  18. Parabolic bundles in positive characteristic. (with Souradeep Majumder) J. Ramanujan Math. Soc. 33 (2018), no. 1, 1-36. pdf-file

  19. Formal orbifolds and orbifold bundles in positive characteristic. (with A. J. Parameswaran) Internat. J. Math. 30 (2019), no. 12, 1950067, 20 pp. arxiv page

  20. Embedding problems for open subgroups of the fundamental group. Ann. Inst. Fourier (Grenoble) 67 (2017), no. 6, 2623-2649. pdf-file

  21. Compositum of wildly ramified extensions. J. Pure Appl. Algebra 218 (2014), no. 8, 1528-1536. pdf-file

  22. Killing wild ramification. Israel J. Math. 199 (2014), no. 1, 421-431. pdf-file

  23. Subgroup structure of fundamental groups in positive characteristic. (with Lior Bary-Soroker) Comm. Algebra, 41 (10), (2013). pdf-file

  24. Fundamental group of affine curves in positive characteristic. J. Algebra 399 (2014), 323-342. pdf-file

  25. Beilinson-Hodge cycles on semiabelian varieties. (with Donu Arapura) Math. Res. Lett. 16 (2009), no. 4, 557--562. pdf-file

  26. Fundamental group in positive characteristic. J. Algebra 319 (2008), no. 12, 5178--5207. pdf

  27. Simultaneous Surface Resolution in Quadratic and Biquadratic Galois Extensions. (with S.S. Abhyankar) Contemporary Mathematics, 390, Dec (2003), 1-8. pdf

  28. Valuations and Rank of Ordered Abelian Groups. Proc. Amer. Math. Soc. 133 (2005), 343-348. pdf


Preprints

Classification of Affine Plane Curves (with Poonam Pokale) preprint available on request.

On the Harder-Narasimhan filtration of the direct image of the structure sheaf (with Indranil Biswas and A. J. Parameswaran) preprint available on request.

The minimum genus of Galois covers of curves (with Poulami Mandal) preprint available on request.

Galois closure of henselization. arxiv page

Cyclicity of certain division algebras over $k(\CC\PP^2)$ (with Rajesh Kulkarni) preprint available on request.

Beilinson-Tate cycles on semi-abelian varieties. (with Donu Arapura) preprint available on request.


Links
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