Related papers: A model for the orbifold Chow ring of weighted pro…

Let $\mathcal{D}$ be a weighted oriented graph and let $I(\mathcal{D})$ be its edge ideal in a polynomial ring $R$. We give the formula of Castelnuovo-Mumford regularity of $R/I(\mathcal{D})$ when $\mathcal{D}$ is a weighted oriented path…

We obtain two classifications of weighted projective spaces; up to homeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the…

We investigate the notion of associated graded coalgebra (algebra) of a bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize those which are bialgebras of type one in the framework of abelian braided monoidal…

We construct positive-genus analogues of Welschinger's invariants for many real symplectic manifolds, including the odd-dimensional projective spaces and the renowned quintic threefold. In some cases, our invariants provide lower bounds for…

We describe bases for the morphism spaces of the Frobenius Heisenberg categories associated to a symmetric graded Frobenius algebra, proving several open conjectures. Our proof uses a categorical comultiplication and generalized cyclotomic…

It was shown by Ostrik (2003) and Natale (2017) that a collection of twisted group algebras in a pointed fusion category serve as explicit Morita equivalence class representatives of indecomposable, separable algebras in such categories. We…

In the first part of the paper Beilinson's theorem on the bounded derived category of coherent sheaves on P^n is extended to weighted projective spaces in a rather explicit form. To this purpose the usual category of coherent sheaves is…

We give bounds on the order of torsion in the Chow group of zero dimensional cycles for isotropic Grassmannians and Brauer-Severi flag varieties. To do this, we introduce tools to understand the behavior of torsion in Chow groups with…

We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from…

All rational homology groups of unordered configuration spaces of the Moebius strip and the projective plane are calculated

Quadrics in the Grassmannian of lines in 3-space form a 19-dimensional projective space. We study the subvariety of coisotropic hypersurfaces. Following Gel'fand, Kapranov and Zelevinsky, it decomposes into Chow forms of plane conics, Chow…

We determine a primitive form for a universal unfolding of an affine cusp polynomial. Moreover, we prove that the resulting Frobenius manifold is isomorphic to the one constructed from the Gromov-Witten theory for an orbifold projective…

We compute rational equivariant Chow rings with respect to a torus of quiver moduli spaces. We derive a presentation in terms of generators and relations, use torus localization to identify it as a subring of the Chow ring of the fixed…

Based on the Basis theorem of Bruhat--Chevalley [C] and the formula for multiplying Schubert classes obtained in [D\QTR{group}{u}] and programed in [DZ$_{\QTR{group}{1}}$], we introduce a new method computing the Chow rings of flag…

A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum of the corresponding weights is no greater than…

Observations on rational Chow groups and cycle class maps in equivariant contexts.

We give a geometric model for the category of coherent sheaves over the weighted projective line of type $(p,q)$ in terms of an annulus with marked points on its boundary. We establish a bijection between indecomposable sheaves over the…

Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that these categories admit a description as Gorenstein projective…

We study, in the context of Voevodsky's triangulated category of motives, several adequate equivalence relations (in the sense of Samuel) on the graded Chow ring $CH^\ast (X\times Y)$ for $X$, $Y$ smooth projective varieties over a field.

In this paper, we study the gravity algebra structure on the negative cyclic homology or the cyclic cohomology of several classes of algebras. These algebras include: Calabi-Yau algebras, symmetric Frobenius algebras, unimodular Poisson…