Tohoku Mathematical Journal
2020

March
SECOND SERIES VOL. 72, NO. 1

Tohoku Math. J.
72 (2020), 127-147

Title SUNADA TRANSPLANTATION AND ISOGENY OF INTERMEDIATE JACOBIANS OF COMPACT KÄHLER MANIFOLDS

Author Carolyn Gordon, Eran Makover, Bjoern Muetzel and David Webb

(Received June 27, 2018)
Abstract. We give a general method for constructing compact Kähler manifolds $X_1$ and $X_2$ whose intermediate Jacobians $J^k(X_1)$ and $J^k(X_2)$ are isogenous for each $k$, and we exhibit some examples. The method is based upon the algebraic transplantation formalism arising from Sunada's technique for constructing pairs of compact Riemannian manifolds whose Laplace spectra are the same. We also show that the method produces compact Riemannian manifolds whose Lazzeri Jacobians are isogenous.

Mathematics Subject Classification. Primary 14K02; Secondary 58G25, 14K30, 32J27, 32Q15, 53C20, 14C30.

Key words and phrases. Intermediate Jacobians, Kähler manifolds, isogeny, Hodge Laplace spectrum, transplantation, Sunada's Theorem.

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