Abstract:
We study the space $M_{n,g}$ of holomorphic $n$-differentials over Riemann
surfaces of genus $g$ for $n>1$. We introduce a set of $n$ vector bundles
over this space, which we call Prym–Tyurin vector bundles.
Corresponding determinant line bundles are called Prym–Tyurin line
bundles. We define a set of $n$ tau-functions on the space $M_{n,g}$ and
interpret them as holomorphic sections of tensor product of certain powers
of Prym–Tyurin line bungles and tautological line bundle. This allows to
express the first Chern classes of Prym–Tyurin line bundles (or
Prym–Tyurin classes) via the boundary classes and the first Chern class of
the tautological line bundle. This is joint work with P.Zograf.
Language: English
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