Related papers: Twisted categorical generic fiber

Consider a finite covering $\beta : C \to X$ of a smooth projective curve $X$ by a reduced, projective, planar curve $C$. Associated to two general polarizations on $C$, $q$ and $q'$, one can construct the corresponding compactified Prym…

Let E be a toric fibration arising from symplectic reduction of a direct sum of line bundles over (almost-) K\"ahler base B. Then each torus-fixed point of the toric manifold fiber defines a section of the fibration. Let L_a be convex line…

We state a conjecture on how to construct affine pavings for cohomologically pure projective algebraic varieties, which admit an action of torus such that the fixed points and $1$-dimensional orbits are finite. Experiments on the affine…

Let $\mathbf{G}$ be a connected reductive group over an algebraically closed field $\mathbb{F}$ of good characteristic, satisfying some mild conditions. In this paper we relate tilting objects in the heart of Bezrukavnikov's exotic…

Given a vector bundle $\mathcal E$ on a smooth projective variety $B$, the flag bundle $\mathcal F l(1,2,\mathcal E)$ admits two projective bundle structures over the Grassmann bundles $\mathcal G r(1, \mathcal E)$ and $G r(2, \mathcal E)$.…

We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y…

We prove the existence of tilting bundles on global quotient stacks that are produced by compatible finite group actions on flat families.

For each pair of elliptic Calabi--Yau $3$-folds in the list of Knapp--Scieidegger--Schimannek \cite{2107.05647}, we prove that they are derived-equivalent linear over the base. Except one self-dual pair, each yields two families of smooth…

We consider a fibration with compact fiber together with a unitarily flat complex vector bundle over the total space. Under the assumption that the fiberwise cohomology admits a filtration with unitary factors, we construct Bismut-Lott…

We give an exposition and generalization of Orlov's theorem on graded Gorenstein rings. We show the theorem holds for non-negatively graded rings which are Gorenstein in an appropriate sense and whose degree zero component is an arbitrary…

The central topic is this question: is a given $k$-\'etale algebra $\prod_lE_l/k$ the specialization of a given $k$-cover $f:X\rightarrow B$ at some point $t_0\in B(k)$? Our main tool is a {\it twisting lemma} that reduces the problem to…

We prove a version of Grothendieck's descent theorem on an `enriched' principal fiber bundle, a principal fiber bundle with an action of a larger group scheme. Using this, we prove the isomorphisms of the equivariant Picard and the class…

We study the algebraic structure of the automorphism group of the derived category of coherent sheaves on a smooth projective variety twisted by a Brauer class. Our main results generalize results of Rouquier in the untwisted case.

We give an introduction to partially wrapped Fukaya categories of surfaces with orbifold singularities. Dissecting an orbifold surface $\mathbf S$ into polygons, certain dissections give rise to formal generators, inducing a triangulated…

Let $\ix$ be a smooth Deligne-Mumford stack over the complex numbers. One can define twisted orbifold Gromov-Witten invariants of $\ix$ by considering multiplicative invertible characteristic classes of various bundles on the moduli spaces…

The Fukaya category of a punctured surface can be reconstructed from a pair-of-pants decomposition using a formal construction that attaches a category to a trivalent graph. We extend this formal construction to include a choice of line…

We show that the theory of derivators (or, more generally, of fibered multiderivators) on all small categories is equivalent to this theory on partially ordered sets, in the following sense: Every derivator (more generally, every fibered…

Using deformation theory of rational curves, we prove a conjecture of Sommese on the extendability of morphisms from ample subvarieties when the morphism is a smooth (or mildly singular) fibration with rationally connected fibers. We apply…

We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao's solution to Varchenko's conjecture on complements of hyperplane…

We study Morita theory of twisted sheaves on $\mu_{n}$-gerbes of line bundles $\mathscr{X}$. In this context, we find explicit equivalent conditions for when two Azumaya algebras on $\mathscr{X}$ are Morita equivalent. Additionally, we…