Families of Wronskian correspondences (Q2717174)

Let \(C\) be a smooth projective complex curve of genus \(g\), and let \(a,b\) be two positive integers with \(a+b=g\). A Wronskian correspondence on \(C\) is the locus \(\text{Wr}(a,b)\) of pairs of points \(P,Q\) such that \(aP+bQ\) is part of a canonical divisor. In this paper under review, the author computes the cycle class of the Wronskian correspondence \(\text{Wr}(a,b)\). Particular attention is paid to the case when \((a,b)=(g-2,2)\). In the last section the author defines the locus \(w(3)\) in \(M_g\), the coarse moduli space of smooth projective curves of genus \(g\), of curves that possess a pair of points \(P,Q\) such that \(Q\) is a ramification point of weight at least three of the linear system \(|K-(g-2)P|\). It is then shown that each irreducible component of \(w(3)\) has the expected codimension \(1\) in \(M_g\). The irreducibility of the locus \(w(3)\) in not known.NEWLINENEWLINEFor the entire collection see [Zbl 0960.00042].