| arXiv:0809.0854 (September 2008) |
| More on superstring chiral measures |
| Francesco Dalla Piazza |
Dipartimento di Scienze Fisiche e Matematiche, Università dell'Insubria, Via Valleggio 11, I-22100 Como, Italia
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| Received. 04 September 2008 Last updated. 04 September 2008 |
| Abstract. In this paper we study the expressions of the superstring chiral measures for $gleq 5$. We obtain certain new expressions which are functions of higher powers of theta constants. For $g=3$ we show that the measures can be written in terms of theta constants to the fourth power and for $g=4$ in term of squares of theta constants. In both cases the forms $Xi_8^{(g)}[0^{(g)}]$ appearing in the expression of the measures are defined on the whole Siegel upper half space. Instead for $ggeq 5$ we find that the measures can no more be expressed as polynomials in the theta constants and are well defined on the moduli space of curves only. We also determine the dimension of certain spaces of modular forms and reinterpret the vanishing of the cosmological constant in terms of group representations. |
| Categories. hep-th math.AG |
| Subject. Algebraic Geometry |
| Comment. 25 pages |
