My research interest is in algebraic geometry. More specifically, I am interested in the following areas.
- Positivity of vector bundles and syzygies of projective varieties.
- ACM and Ulrich vector bundles on projective varieties.
- Hodge theory and singularities in birational geometry.
- Topics related to Fourier-Mukai transforms and generic vanishing theory.
- Deformation theory and geometry of moduli spaces.
Preprints
- Extendable codimension two subvarieties in a general hypersurface, with G. V. Ravindra. [pdf]
- On the local cohomology of secant varieties, with S. Olano. [arXiv]
- Non-existence of low rank Ulrich bundles on Veronese varieties, with A. F. Lopez. [arXiv]
(The Mathematica prints for the relevant computations can be found here.) - Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections, with A. F. Lopez. [arXiv]
(The Mathematica prints for the relevant computations can be found here.) - On partially ample Ulrich bundles, with A. F. Lopez. [arXiv]
Published and accepted articles
- 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, to appear. [arXiv] - Singularities of secant varieties from a Hodge theoretic perspective, with S. Olano, and L. Song.
Proceedings of the London Mathematical Society, to appear. [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: On syzygies of projective bundles on abelian varieties 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 view via the Springer Nature SharedIt Initiative] - 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 view via the Springer Nature SharedIt Initiative] - 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, 118. [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]
