Research

I am interested in algebraic geometry and commutative algebra. In my Ph.D thesis, I worked on a problem based on the toroidalization conjecture. More specifically, my research is focused on the following areas.

• Properties of embeddings of projective varieties in projective spaces, specifically relating to N_p property.
• Local positivity of line bundles on varieties (Seshadri constants).
• Questions on linear systems of plane curves (Nagata and SHGH Conjectures).
• Inequalities involving the Hilbert coefficients of local rings.
• Resolution-type problems in algebraic geometry.

Recent Publications

• Seshadri constants on blow-ups of Hirzebruch surfaces, preprint (with Cyril J. Jacob, Suhas B. N., Amit Kumar Singh).
• Effective cone of a Grassmann bundle over a curve defined over 𝔽_p , to appear in Proc. Indian Acad. Sci. Math. Sci (with Indranil Biswas and Shripad M. Garge). Journal version.
• Seshadri constants of curve configurations on surfaces, preprint (with Praveen Kumar Roy and Aditya Subramaniam).
• Seshadri constants on some flag bundles, to appear in Internat. J. Math. (with Jagadish Pine).
• Some results on Seshadri constants of vector bundles, to appear in Forum. Math. (with Indranil Biswas and Snehajit Misra).
• Seshadri constants of parabolic vector bundles, Doc. Math. 28 (2023), 1163-1190 (with Indranil Biswas, Snehajit Misra and Nabanita Ray). Journal version.
• On the Seshadri constants of equivariant bundles over Bott-Samelson varieties and wonderful compactifications, Manuscripta Math. 173 (2024), no. 1-2, 711-726 (with Indranil Biswas and S. Senthamarai Kannan).
• Seshadri constants on some Quot schemes, Forum Math. 33 (2021), no. 6, 1591-1603 (with Chandranandan Gangopadhyay and Ronnie Sebastian).
• Seshadri constants on Bott towers, J. Algebra 601 (2022), 178-197 (with Indranil Biswas, Jyoti Dasgupta, and Bivas Khan).
• Positivity of vector bundles on homogeneous varieties, Internat. J. Math. 31 (2020), no. 12, 2050097 (with Indranil Biswas and D. S. Nagaraj).
• Weyl and Zariski chambers on projective surfaces, Forum Math. 32 (2020), no. 4, 1027-1037 (with Nabanita Ray).

Students

• Cyril J Jacob (current Ph.D).
• Saketh Heramb Narayanan (Masters, 2023).
• Pratik Roy (Masters, 2023).
• Mukta Vikas Bendke (Masters, 2023).
• Aditya N K Subramaniam (Ph.D, 2021).
• Anant Singh (Masters, 2020).
• Madhuparna Pal (Masters, 2020).
• Abhijit A. J. (Masters, 2019).
• Praveen Kumar Roy (Ph.D, 2019).
• Alapan Mukhopadhyay (Masters, 2017).

Post-docs mentored

• Bivas Khan.
• Suhas B N.
• Amit Kumar Singh.
• Snehajit Misra.
• Nabanita Ray.
• Rupam Karmakar.
• Suratno Basu.
• Krishanu Dan.

Notes

• Lectures on Seshadri constants on surfaces.