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Seshadri constants of Higgs Vector bundles
Krishna Hanumanthu, Snehajit Misra, Nabanita Ray
We define Seshadri constants for Higgs bundles on smooth projective varieties over algebraically closed fields of characteristic zero. This definition is inspired by and analogous…
Positivity of Higgs Vector Bundles
Indranil Biswas, Snehajit Misra, Nabanita Ray
In \cite{BCO25}, Bruzzo, Capasso and Otero extended the notion of ampleness of vector bundles to the more general context of Higgs bundles. But the ampleness of Higgs bundles did n…
Positive cones of -divisor classes
Snehajit Misra, Nabanita Ray
In this article, we define the notion of ample Cartier -divisor classes by using the notion of Seshadri constants for Cartier -divisor classes. In particular, we have shown t…
On Weak bounded negativity conjecture
Snehajit Misra, Nabanita Ray
In the first part of this article, we give bounds on self-intersections of integral curves on blow-ups of surfaces with the anti-cannonical divisor eff…
On Stability of Syzygy Bundles
Snehajit Misra, Nabanita Ray
In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.
Positivity and base loci for vector bundles revisited
Mihai Fulger, Nabanita Ray
We give equivalent descriptions for the augmented and diminished base loci of vector bundles in characteristic zero. We show that these base loci behave well under pullback, tensor…
Slope Semistability and Positive cones of Grassmann bundles
Snehajit Misra, Nabanita Ray
Let be a vector bundle of rank on a smooth complex projective variety . In this article, we compute the nef and pseudoeffective cones of divisors in the Grassmann bundle…
Seshadri constants of parabolic vector bundles
Indranil Biswas, Krishna Hanumanthu, Snehajit Misra +1
Let be a complex projective variety, and let be a parabolic vector bundle on . We introduce the notion of \textit{parabolic Seshadri constants} of . It…
Stability and semi-stability of (2,2)-type surfaces
A. J. Parameswaran, Nabanita Ray
We describe the GIT compactification of the moduli of (2,2)-type effective divisors of (i.e., surfaces of the linear system $\vert π_1^*\mathcal{O}…
Weyl and Zariski chambers on projective surfaces
Krishna Hanumanthu, Nabanita Ray
Let be a nonsingular complex projective surface. The Weyl and Zariski chambers give two interesting decompositions of the big cone of . We study these two decompositions and…
Nef cones of projective bundles over surfaces and Seshadri constants
Snehajit Misra, Nabanita Ray
In this article, we give a description of the closed cone of curves of the projective bundle over a smooth projective variety . Using duality, we then calculate…
Geometry of blown up at seven points
Nabanita Ray
In this paper, we prove that blown up at seven general points admits a conic bundle structure over and it can be embedded as divisor in $\math…