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 Np property.
- Local positivity of line bundles on varieties (Seshadri
- Questions on linear systems of plane curves (Nagata and SHGH
- Inequalities involving the Hilbert coefficients of local rings.
- Resolution-type problems in algebraic geometry.
All my papers are also available on
arXiv at this link.
- Seshadri constants on Bott towers, preprint (with Indranil Biswas, Jyoti Dasgupta, and Bivas Khan).
- Positivity of vector bundles on homogeneous varieties,
to appear in International Journal of Mathematics (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, to appear in Journal of Algebraic Combinatorics (with Brian Harbourne). Full-text view via the Springer Nature SharedIt Initiative.
- Bounded negativity and Harbourne constants on ruled surfaces, to appear in Manuscripta Math. (with Aditya Subramaniam). Full-text view via the Springer Nature SharedIt Initiative.
- Rationality of Seshadri constants on general blow ups of Ρ2, to appear in J. Pure Appl. Algebra (with Łucja Farnik, Jack Huizenga, David Schmitz, and Tomasz Szemberg).
- Seshadri constants and Grassmann bundles over curves, to appear in Annales de l'Institut Fourier (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,
- Toroidalization of locally toroidal morphisms from N-folds to surfaces, J. Pure Appl.
Algebra, 213 (2009), no. 3, 349-359.
- Aditya N K Subramaniam (current Ph.D).
- 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: November 14, 2020