My research interest is in algebraic geometry. More specifically, I am interested in the following areas:
- Hodge theory and singularities in birational geometry
- Arithmetically Cohen-Macaulay (ACM) and Ulrich vector bundles on projective varieties
- Positivity of vector bundles and syzygies of projective varieties
- Topics related to Fourier-Mukai transforms and generic vanishing theory
- Deformation theory and geometry of moduli spaces
Preprints
- A lower bound on the Ulrich complexity of hypersurfaces. (2025)
(with A. F. Lopez)
[arXiv] (Mathematica prints are here: [M1 | M2 | M3 | M4 | M5]) - A Hodge theoretic generalization of Q-homology manifolds. (2025)
(with B. Dirks, and S. Olano)
[arXiv] - On the local cohomology of secant varieties. (2024)
(with S. Olano)
[arXiv] - Non-existence of low rank Ulrich bundles on Veronese varieties. (2024)
(with A. F. Lopez)
[arXiv] (Mathematica prints are here)
Published and accepted articles
- Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections
(with A. F. Lopez)
Transactions of the American Mathematical Society, to appear.
[journal | arXiv]
(Mathematica prints are here, details of the mapping cone construction used in the the journal version is here) - Extendable codimension two subvarieties in a general hypersurface
(with G. V. Ravindra)
Mathematische Zeitschrift, to appear.
[journal | arXiv] - On partially ample Ulrich bundles
(with A. F. Lopez)
Advances in Geometry, to appear.
[journal | arXiv] - Construction of varieties of low codimension with applications to moduli spaces of varieties of general type
(with P. Bangere, F. J. Gallego, and J. Mukherjee)
Journal of the London Mathematical Society (2) 110 (2024), no. 6, Paper No. e70030, 48 pp.
[journal | arXiv] - Singularities of secant varieties from a Hodge theoretic perspective
(with S. Olano, and L. Song)
Proceedings of the London Mathematical Society (3) 129 (2024), no. 4, Paper No. e12635, 34 pp.
[journal | arXiv] - On varieties with Ulrich twisted conormal bundles
(with V. Antonelli, G. Casnati, and A. F. Lopez)
Proceedings of the American Mathematical Society 152 (2024), no. 11, 4645–4658.
[journal | arXiv] - Continuous CM-regularity and generic vanishing, with an appendix by Atsushi Ito
Advances in Geometry 24 (2024), no. 1, 19–37.
[journal | arXiv] - Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces
(with P. Bangere, and J. Mukherjee)
Manuscripta Mathematica 174 (2024), 847–874.
[journal | arXiv | full-text] - On varieties with Ulrich twisted tangent bundles
(with A. F. Lopez)
Annali di Matematica Pura ed Applicata 203 (2024), 1159-1193.
[journal | arXiv | full-text] - Deformations and moduli of irregular canonical covers with K^2=4p_g−8
(with P. Bangere, F. J. Gallego, and J. Mukherjee)
Revista Matemática Complutense 37 (2024), no. 2, 551–602.
[journal | arXiv] - Tautological families of cyclic covers of projective spaces
(with P. Kundu, and J. Mukherjee)
European Journal of Mathematics 9 (2023), no. 4, Paper No. 118, 37 pp.
[journal | arXiv] - A note on stability of syzygy bundles on Enriques and bielliptic surfaces
(with J. Mukherjee)
Proceedings of the American Mathematical Society 150 (2022), no. 9, 3715–3724.
[journal | arXiv] - Smoothing of multiple structures on embedded Enriques manifolds
(with J. Mukherjee)
Mathematische Zeitschrift 300 (2022), no. 2, 1241–1263.
[journal | arXiv] - K3 carpets on minimal rational surfaces and their smoothings
(with P. Bangere, and J. Mukherjee)
International Journal of Mathematics 32 (2021), no. 6, 2150032, 20 pp.
[journal | arXiv] - Remarks on projective normality for certain Calabi-Yau and hyperkähler varieties
(with J. Mukherjee)
Journal of Pure and Applied Algebra 224 (2020), no. 10, 106383, 19 pp.
[journal | arXiv] - On the projective normality and normal presentation on higher
dimensional varieties with nef canonical bundle
(with J. Mukherjee)
Journal of Algebra 540 (2019), 121–155.
[journal | arXiv]
