Related papers: A model for the orbifold Chow ring of weighted pro…
We construct a PROP which encodes 2D-TQFTs with a grading. This defines a graded Frobenius algebra as algebras over this PROP. We also give a description of graded Frobenius algebras in terms of maps and relations. This structure naturally…
We consider the graded space $R$ of syzygies for the coordinate algebra $A$ of projective variety $X=G/P$ embedded into projective space as an orbit of the highest weight vector of an irreducible representation of semisimple complex Lie…
We construct in an abstract fashion the orbifold quantum cohomology (quantum orbifold cohomology) of weighted projective space, starting from the orbifold quantum differential operator. We obtain the product, grading, and intersection form…
For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijection between, on the one hand, the twist-closed…
Motivated by the computation of the BPS-invariants on a local Calabi-Yau threefold suggested by S. Katz, we compute the Chow ring and the cohomology ring of the moduli space of stable sheaves of Hilbert polynomial $4m+1$ on the projective…
Given an algebra with group $G$-action, we construct brace structures for its $G$-twisted Hochschild cochains. An an application, we construct $G$-Frobenius algebras for orbifold Landau-Ginzburg B-models and present explicit orbifold cup…
Linked projective spaces are quiver Grassmanians of constant dimension one of certain quiver representations, called linked nets, over special class of quivers, called $\mathbb{Z}^n$-quivers. They were recently introduced as a tool for…
We first describe a canonical mirror partner (B-model) of the small quantum orbifold cohomology of weighted projective spaces (A-model) in the framework of differential equations: we attach to the A-model (resp. B-model) a D-module on the…
In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations…
We investigate the integral cohomology ring and the Chow ring of the classifying space of the complex projective linear group PGL_p, when p is an odd prime. In particular, we determine its additive structure completely, and we reduce the…
We present an approach to construct a class of generalized Frobenius manifold structures on the orbit spaces of affine Weyl groups, and prove that their monodromy groups are parabolic subgroups of the associated affine Weyl groups.
We construct a two-level weighted TQFT whose structure coefficents are equivariant intersection numbers on moduli spaces of admissible covers. Such a structure is parallel (and strictly related) to the local Gromov-Witten theory of curves…
We prove a formula for the orbifold Chow ring of semi-projective toric DM stacks, generalizing the orbifold Chow ring formula of projective toric DM stacks by Borisov-Chen-Smith. We also consider a special kind of semi-projective toric DM…
Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroids. The support of a representable class can be (partially)…
Following Artin and Zhang's formulation of noncommutative projective geometry, we classify up a family of skew polynomial quadratic algebras up to graded Morita equivalence and their corresponding noncommutative projective spaces up to…
We compute the cohomological Brauer groups of twists of weighted projective spaces and weighted projective stacks.
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
We give a formula for the integral Chow rings of weighted blow-ups. Along the way, we also compute the integral Chow rings of weighted projective stack bundles, a formula for the Gysin homomorphism of a weighted blow-up, and a…
In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…