Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C*

Salomón Rebollo-Perdomo

doi:https://doi.org/10.1016/j.jmaa.2012.05.014

Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C*

Salomón Rebollo-Perdomo

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

Let H be a polynomial of degree m+. 1 on C2 such that its generic fiber is biholomorphic to C*, and let ω be an arbitrary polynomial 1-form of degree n on C2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and ω. © 2012 Elsevier Ltd.

Original language	English
Pages (from-to)	562-570
Journal	Journal of Mathematical Analysis and Applications
Volume	394
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.05.014
Publication status	Published - 15 Oct 2012

Keywords

Abelian integrals
Weak Hilbert's 16th problem

Access to Document

https://doi.org/10.1016/j.jmaa.2012.05.014

https://ddd.uab.cat/record/150520

Cite this

@article{f464f38852dd4fdfbea6d993237f012a,

title = "Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C*",

abstract = "Let H be a polynomial of degree m+. 1 on C2 such that its generic fiber is biholomorphic to C*, and let ω be an arbitrary polynomial 1-form of degree n on C2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and ω. {\textcopyright} 2012 Elsevier Ltd.",

keywords = "Abelian integrals, Weak Hilbert's 16th problem",

author = "Salom{\'o}n Rebollo-Perdomo",

year = "2012",

month = oct,

day = "15",

doi = "https://doi.org/10.1016/j.jmaa.2012.05.014",

language = "English",

volume = "394",

pages = "562--570",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C*

AU - Rebollo-Perdomo, Salomón

PY - 2012/10/15

Y1 - 2012/10/15

N2 - Let H be a polynomial of degree m+. 1 on C2 such that its generic fiber is biholomorphic to C*, and let ω be an arbitrary polynomial 1-form of degree n on C2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and ω. © 2012 Elsevier Ltd.

AB - Let H be a polynomial of degree m+. 1 on C2 such that its generic fiber is biholomorphic to C*, and let ω be an arbitrary polynomial 1-form of degree n on C2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and ω. © 2012 Elsevier Ltd.

KW - Abelian integrals

KW - Weak Hilbert's 16th problem

U2 - https://doi.org/10.1016/j.jmaa.2012.05.014

DO - https://doi.org/10.1016/j.jmaa.2012.05.014

M3 - Article

SN - 0022-247X

VL - 394

SP - 562

EP - 570

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Complete Abelian integrals for polynomials whose generic fiber is biholomorphic to C*

Abstract

Keywords

Access to Document

Fingerprint

Cite this