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Critical dimensions of the string theories and the dualizing sheaf on the moduli space of (super) curves. (English. Russian original) Zbl 0639.14015
Funct. Anal. Appl. 20, 244-246 (1986); translation from Funkts. Anal. Prilozh. 20, No. 3, 88-89 (1986).
The observation in this note, that the critical dimensions 26 and 10 which occur in the theory of strings and superstrings can be observed from the results of D. Mumford [Enseign. Math., II. Ser. 23, 39-110 (1977; Zbl 0363.14003)] on the moduli space of stable curves, has been of fundamental importance in the by now highly developed techniques in string theory. The author suggests also in this paper that the moduli space for $$g\to \infty$$ should play a role for the Virasoro algebra analogous to that of the flag manifold for a simple Lie algebra.
Reviewer: N.J.Hitchin

##### MSC:
 14H15 Families, moduli of curves (analytic) 81T08 Constructive quantum field theory 58D30 Applications of manifolds of mappings to the sciences 14H10 Families, moduli of curves (algebraic)
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##### References:
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