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.

*On the Seshadri constants of equivariant bundles over Bott-Samelson varieties and wonderful compactifications*, preprint (with Indranil Biswas and S. Senthamarai Kannan).*Seshadri constants on some Quot schemes*, to appear in Forum Mathematicum (with Chandranandan Gangopadhyay and Ronnie Sebastian).*Seshadri constants on Bott towers*, preprint (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 Ρ*, J. Pure Appl. Algebra 224 (2020), no. 8, 106345 (with Łucja Farnik, Jack Huizenga, David Schmitz, and Tomasz Szemberg).^{2}*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 Ρ*, J. Pure Appl. Algebra 221 (2017), no. 9, 2372-2382.^{2} *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 Ρ*, J. Algebra 461 (2016), 65-86.^{2} -
*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.

- Cyril J Jacob (current Ph.D).
- 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).

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Last modified: January 14, 2022