A Non-archimedean Analogue of the Calabi-yau Theorem for Totally Degenerate Abelian Varieties
نویسندگان
چکیده
We show an example of a non-archimedean version of the existence part of the Calabi-Yau theorem in complex geometry. Precisely, we study totally degenerate abelian varieties and certain probability measures on their associated analytic spaces in the sense of Berkovich.
منابع مشابه
Calabi–Yau theorem and algebraic dynamics
The aim of this paper is to prove the uniqueness part of the Calabi–Yau theorem for metrized line bundles over non-archimedean analytic spaces, and apply it to endomorphisms with the same polarization and the same set of preperiodic points over a complex projective variety. The proof uses Arakelov theory (cf. [Ar, GS]) and Berkovich’s non-archimedean analytic spaces (cf. [Be]) even though the r...
متن کاملRigidity for Families of Polarized Calabi-yau Varieties
In this paper, we study the analogue of the Shafarevich conjecture for polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs bundles to establish a criterion for the rigidity of families. We then apply the criterion to obtain that some important and typical families of Calabi-Yau varieties are rigid, for examples., Lefschetz pencils of Calabi-Yau varieties, strongly de...
متن کاملThe arithmetic Hodge index theorem for adelic line bundles
In this paper, we prove index theorems for integrable metrized line bundles on projective varieties over complete fields and number fields respectively. As applications, we prove a non-archimedean analogue of the Calabi theorem and a rigidity theorem about the preperiodic points of algebraic dynamical systems.
متن کاملNsf-kitp-03-112 Complex Multiplication of Exactly Solvable Calabi-yau Varieties
We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi-Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi-Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the v...
متن کاملComplex Multiplication of Exactly Solvable Calabi-Yau Varieties
We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi–Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology of the Calabi–Yau manifold, and the conformal field theoretic quantities of the underlying string emerge from the number theoretic structure induced on the v...
متن کامل