Research
My research interests are broadly centered around
Syzygies of algebraic varieties and questions on positivity of linear series
Multiple structures on schemes and their smoothing.
Deformation of finite morphisms and moduli of varieties of general type and their compactification
Rationality of stacks of finite covers of projective spaces.
Publications and Pre-prints:
Projective smoothing of varieties with simple normal crossing (with P. Bangere, F.J. Gallego)(submitted)
2.Construction of varieties of low codimension with applications to moduli spaces of varieties of general type (with P. Bangere, F.J. Gallego and D. Raychaudhury)(submitted)
3.Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on del pezzo surfaces (with P. Bangere, D. Raychaudhury) (manuscripta math(2024). https://doi.org/10.1007/s00229-023-01530-2)
4. Tautological families of cyclic covers of projective spaces (with P. Kundu and D. Raychaudhury)(European Journal of Mathematics, 9, 118, (2023), https://doi.org/10.1007/s40879-023-00703-3)
5. Deformations and moduli of irregular canonical covers with K^2 = 4p_g - 8 (with P. Bangere, F.J. Gallego and D. Raychaudhury) (Rev Mat Complut (2023). https://doi.org/10.1007/s13163-023-00462-5 )
6. A note on stability of syzygy bundles on Enriques and bielliptic surfaces ( with D. Raychaudhury ), (Proc. Amer. Math. Soc. 150 (2022), no. 9, 3715–3724
7. Smoothing of multiple structures on embedded Enriques manifolds ( with D. Raychaudhury) (Math. Z. 300 (2022), no. 2, 1241–1263.)
8. K3 carpets on minimal rational surfaces and their smoothing. (with P. Bangere and D. Raychaudhury) (International Journal of Mathematics 32 (2021), no. 6, 2150032, 20 pp. )
9. Remarks on projective normality and normal presentation for certain Calabi -Yau and hyperk\"ahler varieties. (with D. Raychaudhury)(Journal of Pure and Applied Algebra 224 (2020), no. 10, 106383, 19 pp. )
10. On the projective normality and normal presentation on higher dimensional vatieties with nef canonical bundle. (with D. Raychaudhury)(Journal of Algebra 540 (2019), 121–155. )
In Preparation:
Projective degenerations of K3 surfaces into a union of Hirzebruch surfaces
Syzygies of ribbons on curves (with A. Deopurkar)