04562nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207245018200223250001800405264007500423300006600498336002600564337002600590338003600616347002400652505076100676520181101437650002403248650002803272650002403300650001603324650003603340650002403376650002703400650003903427650005103466700007503517700009103592700008303683700007603766710003403842773002603876776003603902776003603938776003603974856004604010978-3-031-52481-3DE-He21320251030112259.0cr nn 008mamaa240605s2024 sz | s |||| 0|eng d a97830315248137 a10.1007/978-3-031-52481-32doi 4aQA564-609 7aPBMW2bicssc 7aMAT0120102bisacsh 7aPBMW2thema10aHandbook of Geometry and Topology of Singularities V: Foliationsh[electronic resource] /cedited by Felipe Cano, José Luis Cisneros-Molina, Lê Dũng Tráng, José Seade. a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024. aXXVI, 510 p. 73 illus., 29 illus. in color.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 a1 Bruno Scárdua, Holomorphic foliations: singularities and local geometric aspects -- 2 Yu. Ilyashenko, Persistence, uniformizanion and holonomy -- 3 Laura Ortiz-Bobadilla, Ernesto Rosales-González and Sergei Voronin, Holomorphic foliations and vector fields with degenerated singularity in (C2, 0) -- 4 David Marín, Jean-Francois Mattei and Eliane Salem, Topology of singular foliation germs in C2 -- 5 Nuria Corral, Jacobian and polar curves of singular foliations -- 6 Dmitry Novikov and Sergei Yakovenko, Rolle models in the Real and Complex world -- 7 Fernando Sanz Sánchez, Half a century with the problem of the gradient of an analytic function -- 8 Jose Manuel Aroca, Newton Polygon -- 9 Jorge Vitório Pereira, Closed meromorphic 1-forms. aThis is the fifth volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. Singularities are ubiquitous in mathematics and science in general, and singularity theory is a crucible where different types of mathematical problems converge, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. This Volume V focuses on singular holomorphic foliations, which is a multidisciplinary field and a whole area of mathematics in itself. Singular foliations arise, for instance, by considering: The fibers of a smooth map between differentiable manifolds, with singularities at the critical points. The integral lines of a vector field, or the action of a Lie group on a manifold. The singularities are the orbits with special isotropy. The kernel of appropriate 1-forms. The singularities are the zeros of the form. Open books, which naturally appear in singularity theory as foliations with singular set the binding. These important examples highlight the deep connections between foliations and singularity theory. This volume, like its companion Volume VI, also focused on foliations, consists of nine chapters, authored by world experts, which provide in-depth and reader-friendly introductions to some of the foundational aspects of the theory. These introductions also give insights into important lines of further research. The volume starts with a foreword by one of the current world leaders in the theory of complex foliations. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook. 0aAlgebraic geometry. 0aGeometry, Differential. 0aTopological groups. 0aLie groups. 0aFunctions of complex variables.14aAlgebraic Geometry.24aDifferential Geometry.24aTopological Groups and Lie Groups.24aSeveral Complex Variables and Analytic Spaces.1 aCano, Felipe.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aCisneros-Molina, José Luis.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aDũng Tráng, Lê.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aSeade, José.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303152480608iPrinted edition:z978303152482008iPrinted edition:z978303152483740uhttps://doi.org/10.1007/978-3-031-52481-3