Abstract :
Very recently, Grushevsky continued DʹHoker and Phongʹs program of finding the chiral superstring measure from first principles by constructing modular forms satisfying certain factorization constraints. He has proposed an ansatz in genus 4 and conjectured a possible formula for the superstring measure in any genus, subject to the condition that certain modular forms admit holomorphic roots. In this note we want to give some evidence that Grushevskyʹs approach seems to be very fruitful.
