• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

A modular compactification of ℳ1,n from A∞-structures

Journal fuer die reine und angewandte Mathematik. 2019. Vol. 2019. No. 755. P. 151-189.
Polishchuk A., Lekili Y.

We show that a certain moduli space of minimal A∞-structures coincides with the modular compactification ℳ_{1,n}(n−1)of ℳ_{1,n} constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and only if n≤11.