Rational elliptic surfaces and the trigonometry of tetrahedra
نویسندگان
چکیده
We study the trigonometry of non-Euclidean tetrahedra using tools from algebraic geometry. establish a bijection between and certain rational elliptic surfaces. interpret edge lengths dihedral angles tetrahedron as values period maps for corresponding surface. As corollary we show that cross-ratio exponents solid is equal to perimeters its faces. The Regge symmetries are related action Weyl group $$W(D_6)$$ on Picard lattice
منابع مشابه
Rational Points on Elliptic Surfaces
x.1. Elliptic Surfaces Deenition. An elliptic surface consists of a smooth (projective) surface E, a smooth (projective) curve C, and a morphism : E ?! C such that almost all bers E t = ?1 (t) are (smooth projective) curves of genus 1. In addition, we will generally assume that our elliptic surfaces come equipped with an identity section 0 : C ?! E which serves as the identity element of the gr...
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2021
ISSN: ['0020-9910', '1432-1297']
DOI: https://doi.org/10.1007/s00222-021-01066-w