Multiplicity estimates: a Morse-theoretic approach

DOI10.1215/00127094-3165220zbMath1334.14031arXiv1406.1858OpenAlexW3102868281MaRDI QIDQ5963490

Gal Binyamini

Publication date: 22 February 2016

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.1858

zbMATH Keywords

Bernstein-Kushnirenko-Khovanskii boundMilnor fibersmultiplicity estimates for vector fieldspolar varieties

Mathematics Subject Classification ID

Real algebraic sets (14P05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Transcendence (general theory) (11J81) Ordinary differential equations in the complex domain (34M99) Entire functions of several complex variables (32A15) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Diophantine approximation, transcendental number theory (11J99)

Related Items (8)

Rational versus transcendental points on analytic Riemann surfaces ⋮ Multiplicities of Noetherian deformations ⋮ Higher Ramanujan Equations and Periods of Abelian Varieties ⋮ Pfaffian intersections and multiplicity cycles ⋮ Zeroes and rational points of analytic functions ⋮ Some effective estimates for André-Oort in \(Y(1)^n\) ⋮ Finite determination of accessibility and singular points of nonlinear systems: an algebraic approach ⋮ Zero Counting and Invariant Sets of Differential Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiplicity estimates for analytic functions. II
• Trajectories of polynomial vector fields and ascending chains of polynomial ideals
• A bound for the degree of nonholonomy in the plane
• Multiplicities of zeroes of polynomials on trajectories of polynomial vector fields and bounds on degree of nonholonomy
• Algebraic Equations and Convex Bodies
• Oscillation of analytic curves
• Numerical control over complex analytic singularities

This page was built for publication: Multiplicity estimates: a Morse-theoretic approach