arXiv subjects

Bogdan Carasca

Publications and source records attributed to Bogdan Carasca.

3 recordsLinked to original sources

arXiv2026

The Chow ring of $\mathcal{S}_5^-$ is tautological

The moduli spaces $\mathcal{S}_g^-$ parametrise odd spin curves of genus $g$. These are pairs $[C, \eta]$ where $C$ is a smooth genus $g$ curve of and $\eta$ is a line bundle on $C$ such that $\eta^{\otimes 2} = \omega_C$ and $h^0(C, \eta)$ is odd. The main result of this work is the tautology of the Chow ring of $\mathcal{S}_5^-$. Our method of proof revolves around an analysis of the geometry of canonical genus 5 curves and totally tangent hyperplanes. In the course of establishing our main result, we also prove the rationality of the closely related differential stratum in $\mathcal{M}_{5, 4}$ dominating $\mathcal{S}_5^-$.

math.AG↗

arXiv2026

Non--tautological cycles on Prym moduli spaces

We denote by $\mathcal{R}_{g;m}$ the moduli space of $m$--pointed Prym curves of genus $g$, that is, tuples $[\widetilde C / C; x_1, \dots, x_m]$ where $[C, x_1, \dots, x_m]$ is an $m$--pointed curve of genus $g$ and $\widetilde C/ C$ is an \'etale double cover of $C$. In this paper, we address the problem of the non--tautology of the Chow ring of $\mathcal{R}_{g;m}$. The locus which allows us to achieve earlier bounds for the non--tautology of $\mathrm{CH}^\bullet(\mathcal{R}_{g})$ compared to $\mathcal{M}_g$ is the component $\mathcal{R}\mathcal{B}_g^0$ of the locus of bi--elliptic Prym curves. This parametrises covers $[\widetilde C/ C]$ such that, if $C \rightarrow E$ is the bi--elliptic structure, the composition $\widetilde C \rightarrow E$ factors through an elliptic cover of $E$. Our main contribution is thus the non--tautology of the class $[\mathcal{R}\mathcal{B}_8^0] \in \mathrm{CH}^*(\mathcal{R}_8)$. In the course of establishing this theorem, a similar result for the compact moduli spaces $\overline{\mathcal{R}}_{g; 2m}$ for $g + m \geq 8$ is proven.

math.AG↗

arXiv2025

Uniruledness of some moduli spaces of pointed spin curves

The moduli space $\mathcal{S}_{g, 2n}$ parametrizes pointed curves with spin structure. These are tuples $[C, p_1, \dots, p_{2n}, \eta]$ where $\eta \in \text{Pic}(C)$ such that $\eta^{\otimes 2} \cong \omega_C(-p_1 - \dots - p_{2n})$. We prove that $\mathcal{S}_{2, 4}$, $\mathcal{S}_{2, 6}$, $\mathcal{S}_{3, 2}$, $\mathcal{S}_{3, 4}$, $\mathcal{S}_{3, 6}$, $\mathcal{S}_{4, 2}$, $\mathcal{S}_{4, 4}$, $\mathcal{S}_{5, 2}$ and $\mathcal{S}_{5, 4}$ are uniruled.

math.AG↗