We investigate the low degree rational cohomology groups of the moduli space of twisted Prym curves ${\overline{Pr}_{g,n}^{\hspace{0.05cm}(m_1, \ldots, m_n)}} $, where the integer twists $0\leq m_i\leq 1$ have even sum over $i$. We prove that these groups vanish in odd degree $\leq3$ and that the group in degree $2$ is algebraic. In particular, the results cover the classical moduli spaces of Prym curves and Prym curves with simple ramifications.
We consider the moduli stack $\mathcal{H}_{g,d}$ parametrising maps $\theta\colon C\to L$ of degree $d$ between complex curves of genera $g$ and $0$. We provide a splitting of the stable rational cohomology of $\mathcal{H}_{g,d}$, for $g\to\infty$, in terms of degrees of intermediate covers, and identify each direct su...
In this paper, after reviewing recent progress on the cohomology of $\overline{{\cal M}}_{0,n}$, we further our investigation on the cohomology of moduli spaces of pointed curves in continuation of [2,4,5,6,7,8]. In particular, we prove that the Betti number distribution of the Fulton-MacPherson compactification $C[n]$...
We study the $\mathbf{I}^*$-cohomology of a smooth real algebraic curve in terms of its real locus and its geometric genus. We notably extend results of Monnier to the twisted case, which is crucial to the understanding of proper pushforwards of Witt groups. We also perform some computations related to transfers along...
Let $G/P$ be a flag manifold with $G$ simple. We determine the rational homotopy groups $\pi _{\ast }(G/P)\otimes \mathbb{Q}$ and describe the rational cohomology ring $H^{\ast }(G/P;\mathbb{Q})$ solely in terms of the rational homotopy types of $G$ and $P$, respectively. The proof is based on the restrictions of basic...
We investigate the \'etale fundamental group of the complement of a horizontal divisor on $\mathbb{P}^{1}_{\mathbb{Z}}$. We prove that this group has no nontrivial finite solvable quotient if and only if the divisor is normal crossings at the prime~$2$. Moreover, if the divisor is normal crossings at the prime~$2$ and...
Abstract We prove a conjecture of Manin and Orlov: the moduli space script upper M overbar Subscript 0 comma n M¯0,n
$\overline{\mathcal{M}}_{0,n}$
of stable rational curves with n marked points admits a full exceptional collection that is equivariant under the action of the symmetric group upper S Subscript n Sn
$S_n...
Ana-Maria Castravet, J. Tevelev· Compositio Mathematica· 0 citations
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