Complex Analytic Desingularization

DOI10.1007/978-4-431-49822-3zbMath1409.14001OpenAlexW2899222010MaRDI QIDQ4961999

José M. Aroca Hernández Ros, Heisuke Hironaka, J. L. Vicente

Publication date: 29 October 2018

Full work available at URL: https://doi.org/10.1007/978-4-431-49822-3

zbMATH Keywords

Newton polygonsoilvaluationstreescharacteristic conesmodificationsWeierstrass preparation theoremtangent conesforestsinfinitely near singularitiesnormal crossingsmaximal contactnormal flatnessSamuel stratificationThom's conjecturecomplex analytic spacesidealistic exponentsgrovesgardensalléescomplex analytic foliationscontact stability theoremscontinuity of maximal contacthorizontal morphisms, vertical morphisms, cone-fibered spaces, blow-ups, blowing cones, normal conespolygrovesresolution of singularities, hypersurfaces

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Foliations (differential geometric aspects) (53C12) Contact manifolds (general theory) (53D10) Singularities of holomorphic vector fields and foliations (32S65) Foliations in differential topology; geometric theory (57R30) Dynamical aspects of holomorphic foliations and vector fields (37F75) Complex spaces (32C15)

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