Let Mg-bar be the Deligne-Mumford compactification of genus g curves, and let δ1 be the divisor of degenerate curves of the form `genus 1 meeting a genus g-1 transversely".
Question 1: What is the n-fold self intersection of δ1?
I've seen mentioned in the literature that the answer for n = g is
rational curves with g many genus 1 tails. This certainly seems reasonable -- this cycle has the right dimension and is visually' obtained by g-1 many degenerations.
Question 2: Let C be a curve in Mg-bar contained in δ1. How do I calculate the intersection of C and δ1?
I'm interested in the case where C is a family of rational curves with g many fixed elliptic tails (so that each elliptic tail is the same elliptic curve), each with at most two rational components. The answer is in the literature, but without proof. Does anyone know a reference or a quick way to do this calculation?