Multidimensional continued fractions for cyclic quotient singularities and Dedekind sums

DOI10.1215/21562261-2019-0032zbMath1445.11027OpenAlexW2969160168MaRDI QIDQ2175036

Tadashi Ashikaga

Publication date: 27 April 2020

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.kjm/1565402423

zbMATH Keywords

Dedekind sumtoric geometrycontinued fractioncyclic quotient singularity

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Singularities in algebraic geometry (14B05) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Index theory and related fixed-point theorems on manifolds (58J20) Dedekind eta function, Dedekind sums (11F20) Relations with algebraic geometry and topology (11F23) Topology and geometry of orbifolds (57R18)

Related Items (3)

Crepant property of Fujiki-Oka resolutions for Gorenstein abelian quotient singularities ⋮ Fujiki-Oka resolution for three-dimensional cyclic quotient singularities via binary trees ⋮ Hilbert basis resolutions for three-dimensional canonical cyclic quotient singularities

Cites Work

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• Numerical adjunction formulas for weighted projective planes and lattice point counting
• Pseudo-periodic maps and degeneration of Riemann surfaces
• Toroidal embeddings. I
• The Gauss-Bonnet theorem for \(V\)-manifolds
• Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen. (On four-dimensional Riemann surfaces of many-valued analytic functions of two complex variables)
• Toric modifications of cyclic orbifolds and an extended Zagier reciprocity for Dedekind sums
• On formulas for Dedekind sums and the number of lattice points in tetrahedra
• Higher dimensional analogues of periodic continued fractions and cusp singularities
• On semi-regular finite continued fractions
• Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten
• On resolutions of cyclic quotient singularities
• The signature theorem for V-manifolds
• The Riemann-Roch theorem for complex V-manifolds
• Dedekind sums and the signature of \(f(x,y)+z^N\). II
• Toric varieties, lattice points and Dedekind sums
• Hilbert modular surfaces
• Classification of degenerations of curves of genus three via Matsumoto-Montesinos' theorem.
• Deformationen von Quotientensingularitäten (nach zyklischen Gruppen)
• Local signature defect of fibered complex surfaces via monodromy and stable reduction
• Local classification of quotients of complex manifolds by discontinuous groups
• The Jacobi-Perron algorithm its theory and application
• Computing the Continuous Discretely
• Arrangements of curves and algebraic surfaces
• Chern Number Relations for Locally Abelian Galois Coverings of Algebraic Surfaces
• CUSP SINGULARITIES GIVEN BY REFLECTIONS OF STELLABLE CONES
• Geometry of continued fractions

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