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Article

Moduli spaces of nonspecial pointed curves of arithmetic genus 1

Mathematische Annalen. 2017. P. 1-40.
Polishchuk A.

In this paper we study the moduli stack M_{1,n} of curves of arithmetic genus 1 with n marked points, forming a nonspecial divisor. In Polishchuk (A modular compactification of M_{1,n} from A∞-structures, arXiv:1408.0611) this stack was realized as the quotient of an explicit scheme U^{ns}_{1,n} affine of finite type over ℙn−1, by the action of 𝔾m^n . Our main result is an explicit description of the corresponding GIT semistable loci in U^{ns}_{1,n}. This allows us to identify some of the GIT quotients with some of the modular compactifications of M_{1,n} defined in Smyth (Invent Math 192:459–503, 2013; Compos Math 147(3):877–913, 2011).