Manifolds of solutions for Hirzebruch functional equations
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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.
KeywordsSTEKLOV Institute Elliptic Curve Elliptic Curf Elliptic Function Young Diagram
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