A remark on the rational cohomology of S1,n
نویسندگان
چکیده
We focus on the rational cohomology of Cornalba’s moduli space of spin curves of genus 1 with n marked points. In particular, we show that both its first and its third cohomology group vanish and the second cohomology group is generated by boundary classes.
منابع مشابه
On the Associated Primes of the generalized $d$-Local Cohomology Modules
The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary generalized local cohomology modules. Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$ are finitely generated $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...
متن کاملA remark on the means of the number of divisors
We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$, where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$, with $d(n)$ denoting the number of positive divisors of $n$. Also, we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.
متن کاملON GRADED LOCAL COHOMOLOGY MODULES DEFINED BY A PAIR OF IDEALS
Let $R = bigoplus_{n in mathbb{N}_{0}} R_{n}$ be a standardgraded ring, $M$ be a finitely generated graded $R$-module and $J$be a homogenous ideal of $R$. In this paper we study the gradedstructure of the $i$-th local cohomology module of $M$ defined by apair of ideals $(R_{+},J)$, i.e. $H^{i}_{R_{+},J}(M)$. Moreprecisely, we discuss finiteness property and vanishing of thegraded components $H^...
متن کاملCohomology rings of symplectic cuts
The “symplectic cut” construction [Le] produces, from a symplectic manifold M with a Hamiltonian circle action, two symplectic orbifolds C − and C+. We compute the rational cohomology ring of C+ in terms of those of M and C − . 1 Statement of the results Let M be a symplectic n-manifold endowed with an Hamiltonian S1-action with moment map f : M → R. Suppose that 0 is a regular value of f and c...
متن کاملThe Cohomology Rings of the Orbit Spaces of Free Transformation Groups of the Product of Two Spheres
Let G = Zp, p a prime (resp. S1), act freely on a finitistic space X with mod p (resp. rational) cohomology ring isomorphic to that of Sm×Sn. In this paper we determine the possible cohomology algebra of the orbit space X/G.
متن کامل