The question of vanishing of the $\operatorname{BV}$ operator on the cohomology of the moduli space of Riemann surfaces is investigated. The $\operatorname{BV}$ structure, which comprises a $\operatorname{BV}$ operator and an antibracket, is identified, vanishing theorems are proven, and a counter-example is provided.

中文翻译：

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在$ \ operatorname {BV} $结构上模空间的同调性

研究了黎曼曲面的模空间的同调性上的$ \ operatorname {BV} $运算符消失的问题。确定了包含操作符$ \ operatorname {BV} $和反括号的$ \ operatorname {BV} $结构，证明了消失定理，并提供了反例。