Related papers: Stringy Chow rings and weighted blow ups

The logarithmic Hilbert scheme of a logarithmic curve parametrizes subschemes on the expanded degenerations of the curve that are transverse to the boundary. We prove that the logarithmic Hilbert scheme of points on a smooth pointed curve…

We prove a formula for Chow groups of $Quot$-schemes which resolve degeneracy loci of a map between vector bundles, under expected dimension conditions. This result provides a unified way to understand known formulae for various geometric…

This paper is the third and final part of a series devoted to the description of the integral Chow rings of the moduli stacks of hyperelliptic Prym pairs. For a fixed genus $g$, there are two natural stacks, $\mathcal{RH}_g$ and…

This paper is the fourth in a series of four papers aiming to describe the (almost integral) Chow ring of $\overline{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we finally compute the Chow ring of…

Let f: X -> Z be a local, projective, divisorial contraction between normal varieties of dimension n with Q-factorial singularities. Let $Y \subset X$ be a f-ample Cartier divisor and assume that f|Y: Y -> W has a structure of a weighted…

In this paper we study string compactifications on Deligne-Mumford stacks. The basic idea is that all such stacks have presentations to which one can associate gauged sigma models, where the group gauged need be neither finite nor…

In this paper, we compute Chow rings of generically twisted (versal) complete flag varieties corresponding to simple Lie groups

Based on the methods used by the author to prove the Riemann-Roch formula for algebraic stacks, this paper contains a description of the rationnal G-theory of Deligne-Mumford stacks over general bases. We will use these results to study…

We introduce equivariant Chow-Witt groups in order to define Chow-Witt groups of quotient stacks. We compute the Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new…

In this paper certain Chow weight structures on the "big" triangulated motivic categories $DM_R^{eff}\subset DM_R$ are defined in terms of motives of all smooth varieties over the base field. This definition allows studying basic properties…

In this paper we compute the integral Chow ring of the moduli stack $\mathcal{R}_2$ of Prym pairs of genus 2 with integral coefficients.

This paper studies the canonical Chow quotient of a smooth projective variety by a reductive algebraic group. The main purpose is to give some topological interpretations and characterization of Chow quotient which have the advantage to be…

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…

Given a sheaf on a projective space P^n we define a sequence of canonical and easily computable Chow complexes on the Grassmannians of planes in P^n, generalizing the Beilinson monad on P^n. If the sheaf has dimension k, then the Chow form…

We prove a blow-up formula for the generating series of virtual $\chi_y$-genera for moduli spaces of sheaves on projective surfaces, which is related to a conjectured formula for topological $\chi_y$-genera of G\"ottsche. Our formula is a…

In a previous paper we showed that any variety with log-terminal singularities admits a crepant resolution by a smooth Artin stack. In this paper we prove the converse, thereby proving that a variety admits a crepant resolution by a smooth…

Let $X$ be a hyperk\"ahler variety, and let $G$ be a group of finite order non-symplectic automorphisms of $X$. Beauville's conjectural splitting property predicts that each Chow group of $X$ should split in a finite number of pieces. The…

Given a sequence of point and rational curve blow-ups blow-ups of smooth $3-$dimensional projective varieties $Z_{i}$ defined over an algebraically closed field $\mathit{k}$, $Z_{s}\xrightarrow{\pi_{s}}…

This paper is the third in a series of four papers aiming to describe the (almost integral) Chow ring of $\overline{\mathcal{M}}_3$, the moduli stack of stable curves of genus $3$. In this paper, we compute the Chow ring of…

Let $G_k$ be a split algebraic group over $k$. Given a non-trivial $G_k$-torsor $G$, we consider the (twisted) flag variety $F=G/B_k$ for the Borel subgroup $B_k$ containing in $G_k$. The purpose of this paper is the study how to compute…