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

Salomón Rebollo-Perdomo

doi:10.1016/j.jmaa.2012.05.014

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

Salomón Rebollo-Perdomo

Departament de Matemàtiques

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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.

Idioma original	Anglès
Pàgines (de-a)	562-570
Revista	Journal of Mathematical Analysis and Applications
Volum	394
Número	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.05.014
Estat de la publicació	Publicada - 15 d’oct. 2012

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10.1016/j.jmaa.2012.05.014

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

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https://www.scopus.com/pages/publications/84862019802

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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 = "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",

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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

UR - https://www.scopus.com/pages/publications/84862019802

U2 - 10.1016/j.jmaa.2012.05.014

DO - 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*

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