THE COMBINATORICS OF DEGENERATE COVERS AND AN APPLICATION FOR GENERAL CURVES OF GENUS 3

Source abstract

Let Cg be a general curve of genus g. If g≥4 then the monodromy group of a primitive cover Cg→ℙ1 of degree n is either Sn or An, and both cases actually occur (under suitable conditions on n for fixed g). For g=3 also the groups GL32 and AGL32 occur. In the present paper we settle the last possible case of AGL42. This requires new methods (which may be of independent interest) studying the combinatorial structure of degenerate covers.