arXiv subjects
Publications and source records attributed to Valerio Buttinelli.
We give an almost complete classification of Ulrich bundles $\mathcal E$ with $c_2(\mathcal E)^2=0$ on a variety $X$ of dimension $n \ge 4$. Moreover, we show that there are strong constraints on the geometry of $X$ and we study disconnected Ulrich subvarieties.
We study connectedness of degeneracy loci $D_{r-k}(\varphi)$ of morphisms $\varphi : {\mathcal O}_X^{\oplus (r+1-k)} \to \mathcal E$, where $\mathcal E$ is a rank $r$ globally generated bundle on a smooth $n$-dimensional variety $X$ and $k \le 3$. For $k \le 2$ we give a characterization of connectedness in terms of vanishing of Chern classes. Moreover we prove that they are connected, for $k \le \min\{2, r-1,n-1\}$, if $\mathcal E$ is V-big. In the case of Ulrich bundles more precise results are given, both in general and in the case of surfaces.
We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with $q=p_g=0$ and hypersurfaces of dimension $2$ and $3.$
We study the positivity of an Ulrich vector bundle defined with respect to a globally generated ample line bundle. First we prove a generalization of a Lopez theorem on the first Chern class and the bigness of an Ulrich bundle. Then, under some additional assumptions on the polarization, we give a description of its augmented base locus, which consequently leads to a characterization of the V-bigness and of the ampleness of an Ulrich bundle in this setting.