  Very recently, Grushevsky continued D'Hoker and Phong's 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 Grushevsky's
approach seems to be very fruitful.
