Moduli of curves with nonspecial divisors and relative moduli of A_∞-structures

2015/11/12 by Alexander Polishchuk, Polishchuk, Alexander
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1511.03797

v1: 29 pages; v2: 32 pages: added Section 1.3 on the gluing morphism, minor corrections

arxiv created 2016/10/20 · arxiv updated 2016/10/21

Abstract

In this paper for each n≥ g≥ 0 we consider the moduli stack \widetilde\mathcal U^ns_g,n of curves (C,p₁,…,p_n,v₁,…,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 p₁+…+p_n is nonspecial (has no h¹) 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^ns_g,n with a certain relative moduli of A_∞-structures (up to an equivalence) over a family of graded associative algebras parametrized by G(n-g,n).

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