Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Canning, Samir"'
The tautological Chow ring of the moduli space $\mathcal{A}_g$ of principally polarized abelian varieties of dimension $g$ was defined and calculated by van der Geer in 1999. By studying the Torelli pullback of algebraic cycles classes from $\mathcal
Externí odkaz:
http://arxiv.org/abs/2408.08718
Autor:
Canning, Samir
We prove that the tautological rings $\mathsf{R}^*(\overline{\mathcal{M}}_{g,n})$ and $\mathsf{RH}^*(\overline{\mathcal{M}}_{g,n})$ are not Gorenstein when $g\geq 2$ and $2g+n\geq 24$, extending results of Petersen and Tommasi in genus $2$. The proof
Externí odkaz:
http://arxiv.org/abs/2406.10516
Autor:
Arena, Veronica, Canning, Samir, Clader, Emily, Haburcak, Richard, Li, Amy Q., Mok, Siao Chi, Tamborini, Carolina
We prove, for infinitely many values of $g$ and $n$, the existence of non-tautological algebraic cohomology classes on the moduli space $\mathcal{M}_{g,n}$ of smooth, genus-$g$, $n$-pointed curves. In particular, when $n=0$, our results show that the
Externí odkaz:
http://arxiv.org/abs/2402.03874
We define a tautological projection operator for algebraic cycle classes on the moduli space of principally polarized abelian varieties $\mathcal{A}_g$: every cycle class decomposes canonically as a sum of a tautological and a non-tautological part.
Externí odkaz:
http://arxiv.org/abs/2401.15768
We study the Chow ring with rational coefficients of the moduli space $\mathcal F_{2}$ of quasi-polarized $K3$ surfaces of degree $2$. We find generators, relations, and calculate the Chow Betti numbers. The highest nonvanishing Chow group is $\maths
Externí odkaz:
http://arxiv.org/abs/2307.09284
We study collections of subrings of $H^*(\overline{\mathcal{M}}_{g,n})$ that are closed under the tautological operations that map cohomology classes on moduli spaces of smaller dimension to those on moduli spaces of larger dimension and contain the
Externí odkaz:
http://arxiv.org/abs/2307.08830
Autor:
Canning, Samir, Larson, Hannah
The Chow ring of $\mathcal{M}_g$ is known to be generated by tautological classes for $g \leq 9$. Meanwhile, the first example of a non-tautological class on $\mathcal{M}_{g}$ is the fundamental class of the bielliptic locus in $\mathcal{M}_{12}$, du
Externí odkaz:
http://arxiv.org/abs/2209.09715
We prove that the rational cohomology group $H^{11}(\bar{\mathcal{M}}_{g,n})$ vanishes unless $g = 1$ and $n \geq 11$. We show furthermore that $H^k(\bar{\mathcal{M}}_{g,n})$ is pure Hodge-Tate for all even $k \leq 12$ and deduce that $\# \bar{\mathc
Externí odkaz:
http://arxiv.org/abs/2209.03113
Autor:
Canning, Samir, Larson, Hannah
In this paper, we ask: for which $(g, n)$ is the rational Chow or cohomology ring of $\overline{\mathcal{M}}_{g,n}$ generated by tautological classes? This question has been fully answered in genus $0$ by Keel (the Chow and cohomology rings are tauto
Externí odkaz:
http://arxiv.org/abs/2208.02357
Autor:
Canning, Samir, Larson, Hannah
We determine the rational Chow ring of the moduli space $\mathcal{H}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n \leq 2g+6$. We also show that the Chow ring of the partial compactification $\mathcal{I}_{g,n}$, parametrizing
Externí odkaz:
http://arxiv.org/abs/2207.10873