Searcharxiv⌕ Search

arXiv subjects

Pabitra Barik

Publications and source records attributed to Pabitra Barik.

6 recordsLinked to original sources
arXiv2026

Existence of ACM Bundles on Polarized Abelian Varieties

Let \((A, L)\) be a polarized abelian variety of dimension \(g \geq 1\) over an algebraically closed field of characteristic zero. We prove that every nontrivial line bundle \(P\) in the connected component \(\operatorname{Pic}^0(A)\) of the Picard variety is arithmetically Cohen--Macaulay (ACM) with respect to \(L\). For \(g \geq 2\) and any fixed nontrivial \(P \in \operatorname{Pic}^0(A)\), we construct by induction an infinite sequence of indecomposable ACM vector bundles \(E_r\) of every rank \(r \geq 1\). In addition, this paper studies classification questions for ACM line bundles and shows that, for abelian varieties of dimension at least two, the category of ACM bundles is of wild representation type. This paper settles the existence problem for nontrivial ACM bundles on polarized abelian varieties and supply large explicit families of indecomposable examples

math.AG↗
arXiv2026

$IT_0$ sheaves on compactified Jacobian

In this paper we construct stable $IT_{0}$ trosion free sheaves on compactified Jacobian of an integral nodal curve. Our construction is functorial in nature and it provides an uniform method which works for both smooth and nodal curve.

math.AG↗
arXiv2026

Ulrich Sheaves on the Hilbert Square of K3 and Abelian Surfaces

We prove the existence of Ulrich sheaves on the Hilbert scheme of two points on a polarized K3 surface or an abelian surface. The construction proceeds by descending Ulrich bundles on the surface to the symmetric square and lifting them to the Hilbert square via the crepant Hilbert--Chow resolution. Finally, we estimate a bound for Ulrich complexity of the Hilbert Square.

math.AG↗
arXiv2025

On existence of Ulrich sheaf

Let X be a smooth projective variety carrying an Ulrich bundle. In the first part of this note, we construct an Ulrich sheaf on n-th symmetric power of X, which is a singular variety when $DimX >1$. As a consequence, we get the existence of an Ulrich bundle on Hillb^{n}C, where C is a smooth projective curve. Let A be an abelian variety which carries an Ulrich bundle. In the second part of this note, we show the existence of Ulrich bundle on the blow up of $A \times A$ along $A \times \{0\}$.

math.AG↗
arXiv2017

Intersection Poincare polynomial for Nagaraj-Seshadri moduli space

We compute Betti numbers of both the components of the moduli space of rank 2 semi-stable torsion-free sheaves with fixed determinant over a reducible nodal curve with two smooth components intersecting at a node. We also compute the intersection Betti numbers of the moduli space.

math.AG↗