Related papers: Tilting bundles via the Frobenius morphism

In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle…

We prove the (graded) Jordan--H\"{o}lder multiplicities of (mixed) tilting sheaves on flag varieties admit a geometric interpretation as the hypercohomology of certain sheaves on Richardson varieties in the Langlands dual flag variety.…

In this work we study the topology of holomorphic rank two bundles over complex surfaces. We consider bundles that are constructed by glueing and show that under certain conditions the topology of the bundle does not depend on the glueing.…

Let $X$ be a smooth proper genus 2 curve over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the the moduli space $M\_X$ of semi-stable rank 2 vector bundles over $X$, which is…

Let X be a smooth projective curve of genus g \textgreater{}1 defined over an algebraically closed field k of characteristic p \textgreater{}0. For p sufficiently large (explicitly given in terms of r,g) we construct an atlas for the locus…

Let X be a projective smooth irreducible polarized variety over the field of complex numbers. Typical examples of wide extensions are vector bundles E that have a subsheaf F whose slope is much bigger than the slope of E/F, and such that F…

We give a simple combinatorial proof of the toric version of Mori's theorem that the only $n$-dimensional smooth projective varieties with ample tangent bundle are the projective spaces $\mathbb{P}^n$.

Tilting bundles $\mathcal{T}$ on a weighted projective line $\mathbb{X}$ have been intensively studied by representation theorists since they give rise to a derived equivalence between $\mathbb{X}$ and the finite dimensional algebra End…

In this paper, we investigate when there exists a wild hypersurface bundle over a smooth proper toric variety in positive characteristic. In particular, we determine the possibilities for toric varieties with Picard number at most three or…

We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact K\"ahler manifolds. Extending earlier results on non-uniruled projective manifolds by the second and fourth authors, we show that…

Let $\cP=G/P$ be a homogeneous projective variety with $G$ a reductive group and $P$ a parabolic subgroup. In positive characteristic we exhibit for $G$ of low rank a Karoubian complete strongly exceptional poset of locally free sheaves…

Special fibrations of toric varieties have been used by physicists, e.g. the school of Candelas, to construct dual pairs in the study of Het/F-theory duality. Motivated by this, we investigate in this paper the details of toric morphisms…

We prove the existence of tilting objects on generalized Brauer--Severi varieties, some relative flags and some twisted forms of relative flags. As an application we obtain tilting objects on certain homogeneous varieties of classical type…

We find the automorphism group of the moduli space of parabolic bundles on a smooth curve (with fixed determinant and system of weights). This group is generated by: automorphisms of the marked curve, tensoring with a line bundle, taking…

Let $X$ be a very general hypersurface of degree $d$ in the projective $(n+1)$-space with $n \ge 3$, and $f: X \to Y$ a non-birational surjective morphism to a normal projective variety $Y$. We first prove that $Y$ is a klt Fano variety if…

Let \pi : V \rightarrow M be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure (\circ_{M},e_{M}, g_{M}) and typical fiber has the structure of a Frobenius algebra (\circ_{V},e_{V},g_{V}). Using a connection…

Let $k$ be a perfect field of characteristic $p$, and let $X/k$ be a smooth variety. It is known that given a Frobenius lifting of $X$, we can identify prismatic crystals and nilpotent Higgs bundles, known as a positive characteristic…

Resolutions of the diagonal of toric varieties has been an active area of study since Beilinson's celebrated resolution of the diagonal for $\PP^n$ and the disproof of King's conjecture. The author generalized a cellular resolution of the…

The cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels for unimodular projective toric varieties yields a full, strong exceptional collection of line bundles on unimodular projective toric surfaces. The…

Analysis of motion algorithms for autonomous systems operating under variable external conditions leads to the concept of parametrized topological complexity \cite{CFW}. In \cite{CFW}, \cite{CFW2} the parametrized topological complexity was…