Related papers: Strong cycles and intersection products on good mo…

Introduced in [BB], simplicially stable spaces are alternative compactifications of $\mathcal{M}_{g,n}$ generalizing Hassett's moduli spaces of weighted stable curves. We give presentations of the Chow rings of these spaces in genus $0$…

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank,…

Though the Chow group of 0-cycles on a K3 surface is quite large, we observe that the subgroup generated by product of divisors is cyclic.

Let $X$ be a smooth complex projective curve. We prove that there exists a surjective commutative forgetful diagram from the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}_{X}$-twisted rank 2 constrained framed Hitchin…

The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a…

For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow…

We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundles over a smooth projective curve, there are four known…

Using the equivariant virtual cycle of the moduli space of stable maps to [C/Z_r], or equivalently, the vanishing of high-degree Chern classes of a certain vector bundle over the moduli space of stable maps to BZ_r, we derive relations in…

Feng-Yun-Zhang have proved a function field analogue of the arithmetic Siegel-Weil formula, relating special cycles on moduli spaces of unitary shtukas to higher derivatives of Eisenstein series. We prove an extension of this formula in a…

We consider the moduli space $\cSU_C^s(r,\cO_C)$ of rank r stable vector bundles with trivial determinant on a smooth projective curve $C$ of genus $g$. We show that the Abel-Jacobi map on the rational Chow group…

In "Quantization of Hitchin's Integrable System and Hecke Eigensheaves", Beilinson and Drinfeld introduced the "very good" property for a smooth complex equidimensional stack. They prove that for a semisimple complex group G, the moduli…

Using the ring space of sheared Witt vectors, we define certain ring stacks. We suggest several models for the ring stacks. Motivation: there is a conjectural description of the stack of n-truncated Barsotti-Tate groups and its Shimurian…

We describe the moduli space G^r_d of triples consisting of a curve C, a line bundle L on C of degree d, and a linear system V on L of dimension r. This moduli space extends over a partial compactification {\tilde M_g} of M_g inside {\bar…

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…

This paper is the second in a series devoted to describing the integral Chow ring of the moduli stacks $\mathcal{RH}_g$ of hyperelliptic Prym pairs. For fixed genus $g$, the stack $\mathcal{RH}_g$ is the disjoint union of $\lfloor (g+1)/2…

We construct a moduli scheme $F[n]$ that parametrizes tuples $(S_1, S_2, \dots, S_{n+1}, p_1, p_2, \dots, p_n)$ in which $S_1$ is a fixed smooth surface over $\text{Spec } R$ and $S_{i+1}$ is the blowup of $S_i$ at a point $p_i$, $\forall…

We study the injectivity property of certain actions of higher Chow groups on refined unramified cohomology. As an application for every $p\geq1$ and for each $d\geq p+4$ and $n\geq2,$ we establish the first examples of smooth complex…

We present a complete generalization of Kirwan's partial desingularization theorem on quotients of smooth varieties. Precisely, we prove that if $\mathcal{X}$ is an irreducible Artin stack with stable good moduli space $\mathcal{X} \to X$,…

We determine the rational Chow ring of the universal moduli space of rank $2$ semistable bundles over smooth curves of genus $2$, and show that it is generated by certain tautological classes. In the process, we obtain Chow rings of…

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…