## Abstract

For the nth Hirzebruch equation we introduce the notion of universal manifold M_{n} of formal solutions. It is shown that the manifold M_{n}, where n > 1, is algebraic and its dimension is not greater than n + 1. We give a family of polynomials generating the relation ideal in the polynomial ring on M_{n}. In the case n = 2 the generators of this ideal are described. As a corollary we obtain an effective description of the manifold M_{2} and therefore all series determining complex Hirzebruch genera that are fiberwise multiplicative on projectivizations of complex vector bundles. A family of analytic solutions of the second Hirzebruch equation is described in terms of Weierstrass elliptic functions and in terms of Baker–Akhiezer functions of elliptic curves. For this functions the curves differ, yet the series expansions in the vicinity of 0 coincide.

Original language | English |
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Pages (from-to) | 125-137 |

Number of pages | 13 |

Journal | Proceedings of the Steklov Institute of Mathematics |

Volume | 290 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Aug 2015 |

Externally published | Yes |