Samir Canning

Motivic Euler characteristics of moduli spaces of curves

Jonas Bergström, Samir Canning, Dan Petersen +1

A combination of recent results of Canning--Larson--Payne--Willwacher and Payne--Willwacher is that the motivic Euler characteristic of the moduli space $M_{g, n}$ of nonsingular cu…

The Gorenstein property and Pixton's conjecture for compact type moduli

Samir Canning, Hannah Larson, Johannes Schmitt

We show that the tautological ring of $M_{g, n}^{ct}$ is not Gorenstein for $g \geq 2$ and $2 g + n \geq 12$ . We prove new cases of Pixton's conjecture that the $3$ -sp…

The low degree cohomology of compactifications of $A_{g}$

Samir Canning, Dan Petersen, Olivier Taïbi

We compute the low degree $ℓ$ -adic intersection cohomology of symplectic local systems on the Satake compactification of the moduli space $A_{g}$ of principally polarized abelian…

Torelli loci, product cycles, and the homomorphism conjecture for $A_{g}$

Samir Canning, Lycka Drakengren, Jeremy Feusi +7

The tautological $Q$ -subalgebra $R^{*} (A_{g}) \subset CH^{*} (A_{g})$ of the Chow ring of the moduli space of principally polarized abelian va…

math.AG2025

FA-modules of holomorphic forms on $M_{g, n}$

Samir Canning, Hannah Larson, Sam Payne +1

For fixed genus g and varying finite marking set A, the gluing and forgetful maps give the spaces of holomorphic forms on the moduli space of stable A-marked curves of genus g has…

The motivic structures $LS_{12}$ and $S_{16}$ in the cohomology of moduli spaces of curves

Samir Canning, Hannah Larson, Sam Payne +1

We study the appearances of $LS_{12}$ and $S_{16}$ in the weight-graded compactly supported cohomology of moduli spaces of curves. As applications, we prove new n…

Moduli spaces of curves with polynomial point counts

Samir Canning, Hannah Larson, Sam Payne +1

We prove that the number of curves of a fixed genus g over finite fields is a polynomial function of the size of the field if and only if g is at most 8. Furthermore, we determine…

Tautological and non-tautological cycles on the moduli space of abelian varieties

Samir Canning, Dragos Oprea, Rahul Pandharipande

The tautological Chow ring of the moduli space $A_{g}$ of principally polarized abelian varieties of dimension $g$ was defined and calculated by van der Geer in 1999. By st…

The tautological ring of $M_{g, n}$ is rarely Gorenstein

Samir Canning

We prove that the tautological rings $R^{*} (M_{g, n})$ and $RH^{*} (M_{g, n})$ are not Gorenstein when $g \geq 2$ and $2g+n\geq…

math.AG2024★ 1 cited

Holomorphic forms and non-tautological cycles on moduli spaces of curves

Veronica Arena, Samir Canning, Emily Clader +4

We prove, for infinitely many values of $g$ and $n$ , the existence of non-tautological algebraic cohomology classes on the moduli space $M_{g, n}$ of smooth, genus- $g$ , $n…

Tautological projection for cycles on the moduli space of abelian varieties

Samir Canning, Sam Molcho, Dragos Oprea +1

We define a tautological projection operator for algebraic cycle classes on the moduli space of principally polarized abelian varieties $A_{g}$ : every cycle class decompose…

math.AG2023

The Chow ring of the moduli space of degree $2$ quasi-polarized K3 surfaces

Samir Canning, Dragos Oprea, Rahul Pandharipande

We study the Chow ring with rational coefficients of the moduli space $F_{2}$ of quasi-polarized $K 3$ surfaces of degree $2$ . We find generators, relations, and calculate…

math.AG2023★ 3 cited

Extensions of tautological rings and motivic structures in the cohomology of $M_{g, n}$

Samir Canning, Hannah Larson, Sam Payne

We study collections of subrings of $H^{*} (M_{g, n})$ that are closed under the tautological operations that map cohomology classes on moduli spaces of smaller di…

The bielliptic locus in genus 11

Samir Canning, Hannah Larson

The Chow ring of $M_{g}$ is known to be generated by tautological classes for $g \leq 9$ . Meanwhile, the first example of a non-tautological class on $M_{g}$ is t…

math.AG2022★ 3 cited

The eleventh cohomology group of $M ˉ_{g, n}$

Samir Canning, Hannah Larson, Sam Payne

We prove that the rational cohomology group $H^{11} (M ˉ_{g, n})$ vanishes unless $g = 1$ and $n \geq 11$ . We show furthermore that $H^{k} (M ˉ_{g, n})$ is pu…

On the Chow and cohomology rings of moduli spaces of stable curves

Samir Canning, Hannah Larson

In this paper, we ask: for which $(g, n)$ is the rational Chow or cohomology ring of $M_{g, n}$ generated by tautological classes? This question has been fully…

The rational Chow rings of moduli spaces of hyperelliptic curves with marked points

Samir Canning, Hannah Larson

We determine the rational Chow ring of the moduli space $H_{g, n}$ of $n$ -pointed smooth hyperelliptic curves of genus $g$ when $n \leq 2 g + 6$ . We also show that the Chow r…