Complete and computable orbit invariants in the geometry of the affine group over the integers

DOI10.1007/s10231-020-00945-yzbMath1442.13016OpenAlexW3006088829MaRDI QIDQ2196663

Daniele Mundici

Publication date: 3 September 2020

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-020-00945-y

zbMATH Keywords

quadratic formdesingularizationconicconjugate diametersrational polyhedronApollonius of Pergaaffine group over the integersMarkov unrecognizability theorem(Farey)regular simplex\(\mathsf{GL}(n,\mathbb{Z})\)-orbitClifford-Hasse-Witt invariantcomplete orbit invariantHasse-Minkowski theoremHirzebruch-Jung continued fraction algorithmKlein programPappus of Alexandriaregular complexstrong Oda conjectureTuring-computable invariant

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Geometric invariant theory (14L24) Quadratic and bilinear Diophantine equations (11D09) Rational points (14G05) Plane and space curves (14H50) Actions of groups on commutative rings; invariant theory (13A50) Other matrix groups over rings (20H25) Group actions on affine varieties (14R20) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) General binary quadratic forms (11E16)

Uses Software

• CASA

Cites Work

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