A pencil in \({\widetilde {\mathcal M}}_ 6\) with three points at the boundary
The authors show that the pencil of plane sextics \(\{C_ t=W+tD\}\), \(t\in\mathbb{P}^ 1\), where \(W\) is the known (since 1895) Wiman sextic and \(D:xyz(x-y)(x-z)(y-z)=0\), now called Dolgachev sextic, is such that \(\text{Aut}(C_ t)={\mathfrak A}_ 5\), the alternating group, for all \(t\in\mathbb{P}^ 1\). Then they show that the image of this pencil in \(\tilde{\mathcal M}_ 6\), the moduli space of stable curves of genus six, touches the boundary in exactly three points, and they describe the corresponding curves as divisors on the Del Pezzo surface of degree 5.
scientific article; zbMATH DE number 58793