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
- On partially ample Ulrich bundles, with A. F. Lopez. [arXiv]
- Singularities of secant varieties from a Hodge theoretic perspective, with S. Olano, and L. Song. [arXiv]
- On varieties with Ulrich twisted conormal bundles, with V. Antonelli, G. Casnati, and A. F. Lopez. [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. [arXiv]
Published and accepted articles
- 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 (2024). [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 (2023). [journal] [arXiv] [full-text view via the Springer Nature SharedIt Initiative] - 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] - 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 (2023). [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]
