A formula for Mumford measure in superstring theory (Q1263629)

A supersymmetric analogue \(\lambda_{i/2}\) of the Mumford sheaf is defined by taking the Berezinian of the i-th power of a dualizing sheaf. In his study on superstring theory [Funct. Anal. Appl. 20, 244-246 (1986); translation from Funkts. Anal. Prilozh. 20, No.3, 88-89 (1986; Zbl 0639.14015)], \textit{Yu. I. Manin} observed numerical coincidences in string theory and moduli theory of curves, and gave a conjecture which reads \(\lambda_{3/2}=(\lambda_{1/2})^ 5.\) In this note the author gives a sketch of a proof of Manin's conjecture. This paper is used to derive an expression of Mumford supermeasure.