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:
Extendability of general non-prime K3 surfaces without Gaussian maps (with P. Bangere)(submitted)
Syzygies of canonical ribbons on higher genus curves (with A. Deopurkar)(submitted)
Projective smoothing of varieties with simple normal crossing (with P. Bangere, F.J. Gallego)(submitted)
4 . Extendability of projective varieties via degeneration to ribbons with applications to Calabi-Yau threefolds (with P. Bangere)(To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze)
5.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)(J. London Math. Soc. (2) 2024;110:e70030. )
6.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)
7. 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)
8. 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 )
9. 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)
10. Smoothing of multiple structures on embedded Enriques manifolds ( with D. Raychaudhury) (Math. Z. 300 (2022), no. 2, 1241–1263.)
11. 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. )
12. 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. )
13. 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. )
Articles in Preparation:
Geography, deformations and moduli of Z_2^s covers of weighted projective threefolds. (with P. Gallardo)
Extensions of ribbons to carpets. (with A. Deopurkar)
Extendability of general K3 surfaces without Gaussian maps and classification of prime Fano threefolds.
Extendability of canonical surfaces on the Castelnuovo line. (with P. Bangere)
Talks and Posters:
Upcoming Conference talk: Summer Research Institute, Colorado State University, Extendability of general K3 surfaces without Gaussian maps and classification of non-prime Fano threefolds.
Invited talk: Algebra Seminar, Auburn University, Syzygies of canonical ribbons on higher genus curves.
Conference talk: AMS Special session, University of California, Riverside, Projective smoothing of varieties with simple normal crossing and applications to extendability of projective varieties.
Invited talk: Algebraic Geometry Seminar, Australian National University, Projective smoothing of varieties with simple normal crossing and applications to extendability of projective varieties.
Conference talk: Commutative Algebra and Algebraic Geometry in TUcSon, University of Arizona, Projective smoothing of varieties with simple normal crossing.
Invited talk: NCTS Seminar in Birational Geometry, National Taiwan University, Deformations and moduli of irregular canonical covers with K^2 = 4p_g-8.
Invited talk: Seminar on Commutative Algebra and Algebraic Geometry, University of California at Berkeley, Deformations and moduli of irregular canonical covers with K^2 = 4p_g-8.
Invited talk: Geometry Seminar at Roma Tre, Università degli studi Roma Tre, Deformations and moduli of irregular canonical covers with K^2 = 4p_g-8.
Invited talk: Fields Number Theory Seminar, The Fields Institute for Research in Mathematical Sciences, Tautological families of cyclic covers of projective spaces.
Invited talk: Brown Algebraic Geometry Seminar, Brown University, Deformations and moduli of irregular canonical covers with K^2 = 4p_g-8.
Conference talk: Kansas Geometry Day, University of Kansas, Deformations and moduli of irregular canonical covers with K^2 = 4p_g-8.
Invited talk: Algebraic Geometry seminar, University of California at Riverside, Deformations and moduli of irregular canonical covers with K^2 = 4p_g-8.
Conference talk: MAGGC, University of Illinois at Chicago, Deformations of Quadruple Galois Canonical Covers.
Poster Presentation: Western Algebraic Geometry Symposium, University of Utah, Smoothing of multiple structures on embedded Enriques manifolds.