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.

Publications (arXiv link)

Rationality of Seshadri constants on blow-ups of ruled surfaces, preprint (with Cyril J. Jacob, Suhas B. N., Amit Kumar Singh).
Seshadri constants on blow-ups of Hirzebruch surfaces, to appear in Math. Nachr. (with Cyril J. Jacob, Suhas B. N., Amit Kumar Singh).
Effective cone of a Grassmann bundle over a curve defined over 𝔽_p , Proc. Indian Acad. Sci. Math. Sci. 134 (2024), no. 1, Paper No. 8 (with Indranil Biswas and Shripad M. Garge). Journal version.
Seshadri constants of curve configurations on surfaces, to appear in Taiwanese J. Math. (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, Forum. Math. 36 (2024), no.3, 641-653 (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).
Negative curves on special rational surfaces, Analytic and Algebraic Geometry 3, 67-78, Łódź University Press, Łódź, 2019 (with Marcin Dumnicki, Łucja Farnik, Grzegorz Malara, Tomasz Szemberg, Justyna Szpond, and Halszka Tutaj-Gasińska).
Real and complex supersolvable line arrangements in the projective plane, Journal of Algebraic Combinatorics 54 (2021), 767-785 (with Brian Harbourne). Full-text view via the Springer Nature SharedIt Initiative.
Bounded negativity and Harbourne constants on ruled surfaces, Manuscripta Math. 164 (2021), no. 3-4, 431-454 (with Aditya Subramaniam). Full-text view via the Springer Nature SharedIt Initiative.
Rationality of Seshadri constants on general blow ups of Ρ², J. Pure Appl. Algebra 224 (2020), no. 8, 106345 (with Łucja Farnik, Jack Huizenga, David Schmitz, and Tomasz Szemberg).
Seshadri constants and Grassmann bundles over curves, Annales de l'Institut Fourier, 70(4):1477-1496, 2020 (with Indranil Biswas, D. S. Nagaraj, and Peter E. Newstead). Journal version.
Seshadri constants on hyperelliptic surfaces, Proc. Amer. Math. Soc. 146 (2018), no. 10, 4175-4187 (with Praveen Kumar Roy).
Single point Seshadri constants on rational surfaces, J. Algebra 499 (2018), 37-42 (with Brian Harbourne).
Multi-point Seshadri constants on ruled surfaces, Proc. Amer. Math. Soc. 145 (2017), no. 12, 5145-5155 (with Alapan Mukhopadhyay).
Positivity of line bundles on special blow ups of Ρ², J. Pure Appl. Algebra 221 (2017), no. 9, 2372-2382.
Seshadri constants on surfaces with Picard number 1, Manuscripta Math. 153 (2017), no. 3-4, 535-543. Full-text view via the Springer Nature SharedIt Initiative.
Positivity of line bundles on general blow ups of Ρ², J. Algebra 461 (2016), 65-86.
Syzygies of some GIT quotients, J. Ramanujan Math. Soc. 31 (2016), no. 4, 419-430 (with S. Senthamarai Kannan).
Syzygies of surfaces of general type, Geom. Dedicata 167 (2013), 123-149 (with P. Bangere).
Bounding the first Hilbert coefficient, Proc. Amer. Math. Soc. 140 (2012), no. 1, 109-117 (with Craig Huneke).
Some Koszul rings from geometry, J. Algebra, 323 (2010), no. 2, 526-539.
Toroidalization of locally toroidal morphisms from N-folds to surfaces, J. Pure Appl. Algebra, 213 (2009), no. 3, 349-359.

Students

Cyril J Jacob (current Ph.D).
Saketh Heramb Narayanan (Okounkov bodies, 2023 Masters).
Pratik Roy (Completions, Cohen Structure Theorem, Hensel's Lemma and some applications in Algebraic Geometry, Masters, 2023).
Mukta Vikas Bendke (Hilbert functions and Bézout's theorem, Masters, 2023).
Aditya N K Subramaniam (Bounded negativity and Harbourne constants on algebraic surfaces, Ph.D, 2021).
Anant Singh (Containment properties of symbolic powers and ordinary powers, Masters, 2020).
Madhuparna Pal (Hilbert functions of local rings, Masters, 2020).
Abhijit A. J. (Sheaf cohomology and Serre duality, Masters, 2019).
Praveen Kumar Roy (Seshadri constants on algebraic surfaces, Ph.D, 2019).
Alapan Mukhopadhyay (Multi-point Seshadri constants on surfaces, 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.

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Last modified: October 29, 2024