An algebraic algorithm for the resolution of singularities of foliations

DOI10.1007/s00200-008-0084-yzbMath1189.37057OpenAlexW2155637074MaRDI QIDQ733712

D. Kharzeev

Publication date: 19 October 2009

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-008-0084-y

zbMATH Keywords

algorithmresolution of singularitiesblow upfoliationsGroebner bases

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Singularities of holomorphic vector fields and foliations (32S65) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Uses Software

• SINGULAR

Cites Work

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• On the classification of simple quadratic derivations over the affine plane
• A rational approach to the Prelle-Singer algorithm
• The Poincaré problem in the nondicritical case
• Hilbert modular foliations on the projective plane
• Elementary First Integrals of Differential Equations
• Isolated invariant curves of a foliation
• DIFFERENTIALLY SIMPLE RINGS WITH NO INVERTIBLE DERIVATIVES
• Reduction of Singularities of the Differential Equation Ady = Bdx

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