A modular compactification of ${\mathcal{M}}_{1,n}$ from $A_{\infty }$-structures

Yanki Lekili, Alexander Polishchuk

We show that a certain moduli space of minimal $A_{\infty }$-structures coincides with the modular compactification ${\bar{\mathcal{M}}}_{1,n}(n-1)$ of ${\mathcal{M}}_{1,n}$ constructed b…