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MODULI OF CURVES WITH NONSPECIAL DIVISORS AND RELATIVE MODULI OF $A_{\infty }$-STRUCTURES
Published online by Cambridge University Press: 30 October 2017
Abstract
In this paper, for each $n\geqslant g\geqslant 0$ we consider the moduli stack $\widetilde{{\mathcal{U}}}_{g,n}^{ns}$ of curves $(C,p_{1},\ldots ,p_{n},v_{1},\ldots ,v_{n})$ of arithmetic genus $g$ with $n$ smooth marked points $p_{i}$ and nonzero tangent vectors $v_{i}$ at them, such that the divisor $p_{1}+\cdots +p_{n}$ is nonspecial (has $h^{1}=0$) and ample. With some mild restrictions on the characteristic we show that it is a scheme, affine over the Grassmannian $G(n-g,n)$. We also construct an isomorphism of $\widetilde{{\mathcal{U}}}_{g,n}^{ns}$ with a certain relative moduli of $A_{\infty }$-structures (up to an equivalence) over a family of graded associative algebras parametrized by $G(n-g,n)$.
MSC classification
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 6 , November 2019 , pp. 1295 - 1329
- Copyright
- © Cambridge University Press 2017
Footnotes
Supported in part by the NSF grant DMS-1400390 and by the Russian Academic Excellence Project ‘5-100’.
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