Related papers: The bielliptic locus in genus 11

We define the tautological ring as the subring of the Chow ring of a Shimura variety generated by all Chern classes of all automorphic bundles. We explain its structure for the special fiber of a good reduction of a Shimura variety of Hodge…

We show that any degree at least $g$ polynomial in descendant or tautological classes vanishes on $M_{g,n}$ when $g\ge 2$. This generalizes a result of Looijenga and proves a version of Getzler's conjecture. The method we use is the study…

Given a reductive group, choice of maximal torus and Borel subgroup, and two subsets of the simple roots, one obtains a closed embedding of sub flag varieties. In this paper we compute the class of the sub flag variety in the Chow ring for…

We consider a $10$-dimensional family of Lehn-Lehn-Sorger-van Straten hyperk\"ahler eightfolds which have a non-symplectic automorphism of order $3$. Using the theory of finite-dimensional motives, we show that the action of this…

We study tautological classes on the moduli space of stable $n$-pointed hyperelliptic curves of genus $g$ with rational tails. Our result gives a complete description of tautological relations. The method is based on the approach of Yin in…

Given a connected, reductive $\mathbf{F}_p$-group $G$, a cocharacter $\mu \in X_*(G)$ and a smooth zip period map $\zeta:X \to \mathop{\text{$G$-{\tt Zip}}}\nolimits^{\mu}$, we study which classes in the Wedhorn-Ziegler tautological rings…

Let $\L_g^G$ denote the locus of hyperelliptic curves of genus $g$ whose automorphism group contains a subgroup isomorphic to $G$. We study spaces $\L_g^G$ for $G \iso \Z_n, \Z_2{\o}\Z_n, \Z_2{\o}A_4$, or $SL_2(3)$. We show that for $G \iso…

This chapter provides a comprehensive survey of foundational results and recent advances concerning minimal generating sets for the mapping class group of a nonorientable surface, $\mathrm{Mod}(N_{g})$, and its index-two twist subgroup,…

Let $[\overline{\mathcal{B}}_{2,0,20}]$ and $[\mathcal{B}_{2,0,20}]$ be the classes of the loci of stable resp. smooth bielliptic curves with 20 marked points where the bielliptic involution acts on the marked points as the permutation (1…

We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results…

We construct explicit examples of algebraic cycles in \bar M_g (for large g congruent to 2 mod 4) and in M_2,20 (no bar) which are not in the tautological ring. In an appendix we give a general method for computing intersections in the…

We compute the integral Chow ring of the quotient stack $[(\mathbb{P}^1)^n/PGL_2]$, which contains $\mathcal{M}_{0,n}$ as a dense open, and determine a natural $\mathbb{Z}$-basis for the Chow ring in terms of certain ordered incidence…

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…

For unitary, orthogonal and symplectic groups, we compute the dimension of the reduced Emerton-Gee stacks, and give an explicit description of their top-dimensional Chow group. Our results are unconditional when $p\neq 2$. The main…

We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

We study a graded algebra D=D(L,G) defined by a finite lattice L and a subset G in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De…

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 $0$…

Genus $g$ Torelli space is the moduli space of genus $g$ curves of compact type equipped with a homology framing. The hyperelliptic locus is a closed analytic subvariety consisting of finitely many mutually isomorphic components. We use…

Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show…

We use relations in the tautological ring of the moduli spaces $\overline{\mathcal{M}}_{g,n}$ derived by Pandharipande, Pixton, and Zvonkine from the Givental formula for the $r$-spin Witten class in order to obtain some restrictions on the…