Related papers: On varieties with Ulrich twisted normal bundles

In this paper, we consider the existence problem of Ulrich bundles on a rational homogeneous space $G/P$ of type $B$, $C$ or $D$. We show that if the Picard number of $G/P$ is greater than or equal to $2$, then there are no irreducible…

We show that local complete intersection subvarieties of smooth projective varieties, which have partially ample normal bundle, possess the G2-property. This generalizes results of Hartshorne and B\u{a}descu-Schneider.

We study Hodge bundles on Siegel varieties and their various extensions to smooth toroidal compactifications. Precisely, we construct a canonical Hodge bundle on an arbitrary Siegel variety so that the holomorphic tangent bundle can be…

Let X be a standard determinantal scheme X \subset \PP^n of codimension c, i.e. a scheme defined by the maximal minors of a t \times (t+c-1) homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf…

We give a complete list of smooth and rationally smooth normalized Schubert varieties in the twisted affine Grassmannian associated with a tamely ramified group and a special vertex of its Bruhat-Tits building. The particular case of the…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

In this article, we introduce the notion of periodic de Rham bundles over smooth complex curves. We prove that motivic de Rham bundles over smooth complex curves are periodic. We conjecture that irreducible periodic de Rham bundles over…

We develop the theory of twisted L^2-cohomology and twisted spectral invariants for flat Hilbertian bundles over compact manifolds. They can be viewed as functions on the first de Rham cohomology of M and they generalize the standard…

Let G be a complex reductive group. A normal G-variety X is called spherical if a Borel subgroup of G has a dense orbit in X. Of particular interest are spherical varieties which are smooth and affine since they form local models for…

An Ulrich sheaf on an embedded projective variety is a normalized arithmetically Cohen-Macaulay sheaf with the maximum possible number of independent sections. Ulrich sheaves are important in the theory of Chow forms, Boij-Soderberg theory,…

We prove that certain quiver varieties are irreducible and therefore are isomorphic to Hilbert schemes of points of the total spaces of the bundles $\mathcal O_{\mathbb P^1}(-n)$ for $n \ge 1$.

We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…

Given a smooth del Pezzo surface $X_d \subseteq \mathbb{P}^{d}$ of degree $d,$ we show that a smooth irreducible curve $C$ on $X_d$ represents the first Chern class of an Ulrich bundle on $X_d$ if and only if its kernel bundle $M_C$ admits…

For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles…

In this paper, we consider the existence problem of rank one and two stable Ulrich bundles on imprimitive Fano 3-folds obtained by blowing-up one of $\mathbb{P}^{3}$, $Q$ (smooth quadric in $\mathbb{P}^{4}$), $V_{3}$ (smooth cubic in…

We prove that on closed manifolds of odd Euler characteristic fixed point sets of involutions are smoothly nondisplaceable.

We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures,…

This paper generalises Mori's famous theorem about "Projective manifolds with ample tangent bundles" to normal projective varieties in the following way: A normal projective variety over $\mathbb{C}$ with ample tangent sheaf is isomorphic…

Let X be a geometrically irreducible smooth projective curve over a field k. We describe the algebra of endomorphisms of indecomposable unstable vector bundles over X of rank 2 and degree d. Fixing some numerical invariants, namely the…

In this paper, we characterize Ulrich modules over cyclic quotient surface singularities by using the notion of special Cohen-Macaulay modules. We also investigate the number of indecomposable Ulrich modules for a given cyclic quotient…