Related papers: Koszul duality for toric varieties

This paper is devoted to an exposition of the Koszul complex of a supermodule and its Berezinian from an intrinsic and as general as possible point of view. As an application, an analogue to Bott's formula in the supercommutative setting…

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…

In this paper, we construct a bar-cobar adjunction and a Koszul duality theory for protoperads, which are an operadic type notion encoding faithfully some categories of bialgebras with diagonal symmetries, like double Lie algebras (DLie).…

We give a complete (global) characterization of complex perverse sheaves on semi-abelian varieties in terms of their cohomology jump loci. Our results generalize Schnell's work on perverse sheaves on complex abelian varieties, as well as…

Using truncated convolution of perverse sheaves on a flag variety Lusztig associated a monoidal category to a two sided cell in the Weyl group. We identify this category in the case which was not decided previously.

For each integer $k\geq 4$ we describe diagrammatically a positively graded Koszul algebra $\mathbb{D}_k$ such that the category of finite dimensional $\mathbb{D}_k$-modules is equivalent to the category of perverse sheaves on the isotropic…

Continuing the study of perverse sheaves on the nilpotent cone of a $\mathbb{Z}/m$-graded Lie algebra initiated by Lusztig--Yun, we study in this work the parabolic induction and introduce the notion of supercuspidal sheaves on the…

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the…

We construct a generalization of Koszul duality in the sense of Keller--Lef\`evre for not necessarily augmented algebras. This duality is closely related to classical Morita duality and specializes to it in certain cases.

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example…

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves…

In this paper we study a category of trees TI and prove that it is a Koszul category. Consequences are the interpretation of the reduced bar construction of operads of Ginzburg and Kapranov as the Koszul complex of this category, and the…

The notion of higher order dual varieties of a projective variety, introduced in \cite{P83}, is a natural generalization of the classical notion of projective duality. In this paper we present geometric and combinatorial characterizations…

We describe the weight filtration in the cohomology of toric varieties. We present a role of the Frobenius automorphism in an elementary way. We prove that equivariant intersection homology of an arbitrary toric variety is pure. We obtain…

We study the curved Koszul duality theory for associative algebras presented by quadratic-linear-constant (QLC) relations. As an application, we investigate the cyclic (co)homology of a QLC algebra and its Koszul dual curved DG algebra, and…

This is an extended example of the study of mirror symmetry via log schemes and the discrete Legendre transform on affine manifolds, introduced by myself and Bernd Siebert in "Mirror Symmetry via Logarithmic Degeneration Data I"…

We describe diagrammatically a positively graded Koszul algebra \mathbb{D}_k such that the category of finite dimensional \mathbb{D}_k-modules is equivalent to the category of perverse sheaves on the isotropic Grassmannian of type D_k…

We generalize the theory of Koszul complexes and Koszul algebras (in particular, Koszul duality between symmetric and exterior algebras) to symmetric tensor categories. In characteristic $p\ge 5$, this theory exhibits peculiar effects, not…

In this article we discuss two different but related results on Hochschild (co)homology and the theory of Koszul duality. On the one hand, we prove essentially that the Tamarkin-Tsygan calculus of an Adams connected augmented dg algebra and…

We investigate Koszul cohomology on irreducible nodal curves. In particular, we prove both Green and Green-Lazarsfeld conjectures for the general k-gonal nodal curve.