arXiv subjects
Publications and source records attributed to Poornapushkala Narayanan.
In this article, we prove that any smooth projective variety $X$ which is a double cover of the projective space $\mathbb{P}^n$ ($n\geq 2$) admits an Ulrich bundle. When $n=2$, we show that on any such $X$, there is an Ulrich bundle of rank two.
Consider a smooth complex surface $X$ which is a double cover of the projective plane $\mathbb{P}^2$ branched along a smooth curve of degree $2s$. In this article, we study the geometric conditions which are equivalent to the existence of Ulrich line bundles on $X$ with respect to this double covering. Also, for every $s\geq 1$, we describe the classes of such surfaces which admit Ulrich line bundles and give examples.
Our aim in this article is to produce new examples of semistable Lazarsfeld- Mukai bundles on smooth projective surfaces $X$ using the notion of parabolic vector bundles. In particular, we associate natural parabolic structures to any rank two (dual) Lazarsfeld-Mukai bundle and study the parabolic stability of these parabolic bundles. We also show that the orbifold bundles on Kawamata coverings of $X$ corresponding to the above parabolic bundles are themselves certain (dual) Lazarsfeld-Mukai bundles. This gives semistable Lazarsfeld-Mukai bundles on Kawamata covers of the projective plane and of certain K3 surfaces.
Consider an ample and globally generated line bundle $L$ on a smooth projective variety $X$ of dimension $N\geq 2$ over $\mathbb{C}$. Let $D$ be a smooth divisor in the complete linear system of $L$. We construct reflexive sheaves on $X$ by an elementary transformation of a trivial bundle on $X$ along certain globally generated torsion-free sheaves on $D$. The dual reflexive sheaves are called the Lazarsfeld-Mukai reflexive sheaves. We prove the $μ_L$-(semi)stability of such reflexive sheaves under certain conditions.
Let $X$ be the Jacobian of a genus 2 curve $\widetilde{\mathcal{C}}$ over $\mathbb{C}$ and $Y$ be the associated Kummer surface. Consider an ample line bundle $L=O(m\widetilde{\mathcal{C}})$ on $X$ for an even number $m$, and its descent to $Y$, say $L'$. We show that any dominating component of $\mathcal{W}^1_{d}(|L'|)$ corresponds to $μ_{L'}$-stable Lazarsfeld-Mukai bundles on $Y$. Further, for a smooth curve $C \in |L|$ and a base-point free $g^1_d$ on $C$, say $(A,V)$, we study the $μ_L$-semistability of the rank-2 Lazarsfeld-Mukai bundle associated to $(C,(A,V))$ on $X$. Under certain assumptions on $C$ and the $g^1_d$, we show that the above Lazarsfeld-Mukai bundles are $μ_L$-semistable.