Algebro-geometric solutions of the string equation

Details Algebro-geometric solutions of the string equation Algebro-geometric solutions of the string equation

2011-10-04

arxiv.org/abs/1110.0729v1

Mathematics

Algebraic Geometry

46 pages

Scientific paper

We will describe algebro-geometric solutions of the KdV hierarchy whose $\tau$-functions in addition satisfy the so-called Virasoro constraints (in particular, the string equation). We show that these solutions are closely related to embeddings of the positive half of the Virasoro algebra into the Lie algebra of differential operators on the circle as well as to double covers of the projective line equipped with a line bundle. As by-products, we exhibit certain links of our methods with $\Gl(n)$-opers on the punctured disk and with the Virasoro constraints appearing in 2D quantum gravity.

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