arXiv subjects
Publications and source records attributed to Federico Tufo.
We study the weak Brill--Noether problem for vector bundles on nodal Enriques surfaces by exploiting the classical realization of a nodal Enriques surface $X$ as a Reye congruence in the Grassmannian $\operatorname{Gr}(2,4)$. We consider restrictions of irreducible homogeneous bundles from the ambient Grassmannian and study their behavior with respect to the weak Brill--Noether property and slope stability.
We compute the Brauer group of some of the known Enriques manifolds. We then build special Brauer-Severi varieties on these manifolds and study the pull-back map from the Brauer group of an Enriques manifold to that of its hyper-K\"ahler universal cover, from both a geometric and an algebraic perspective.
We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface from six to four.
Let X be a very general Debarre--Voisin fourfold. In this article, we prove that all the Schur functors of the restriction of the quotient bundle of Gr(6,10) to X are modular and polystable vector bundles. We also show that the atomic bundles among them are exactly the symmetric powers of the restriction of the quotient bundle. Moreover, we compute the Ext}-groups of different modular vector bundles on X, and we find examples with non-trivial dimensional first Ext}-group.
In this paper, we study 170 families of quiver flag zero loci Fano fourfolds as described by Kalashnikov. We interpret those manifolds as zero loci of sections of homogeneous vector bundles in homogeneous varieties, and we give a birational and biregular description of all 170 families.