arXiv subjects
Publications and source records attributed to Călin Spiridon.
This note addresses the resonance of monomial subspaces. In the first part, we completely characterize the cases where the Fitting scheme structure of the resonance associated with a monomial subspace is reduced, and we further investigate the primary decomposition of the corresponding Fitting ideal. The second part focuses on non-monomial subspaces having the resonance of a monomial subspace.
In this note, we study the resonance variety of rank-two vector bundles over an elliptic curve. Our approach is based on analyzing the flattening stratification of the resonance. We also investigate the linear section of the Grassmann variety $\operatorname{Gr}(2,n)$ from which the resonance is constructed through the lens of its corresponding flattening stratification.
This work revolves around the question of whether a given resonance variety is associated with a vector bundle. We show the existence of a family of natural morphisms on a stratification of the resonance variety to a suitable family of a Quot scheme and provide some applications in the curve case. The existence of this family of morphisms represents an obstruction to affirmatively answering the main question. In addition, we study the resonance of restricted universal rank-two quotient bundles over transversal linear sections of the Grassmann varieties $\operatorname{Gr}_2(\mathbb{C}^n)$, with a special attention to low-dimensional Grassmannians. These bundles are among the most natural to consider in this context. The analysis for $\operatorname{Gr}_2(\mathbb{C}^6)$ shows that any resonance variety in $\mathbb{P}^5$ consisting of fourteen disjoint lines is the resonance of some bundle which appeared in the work of Mukai.