On the factorization of the polar of a plane branch

A. Hefez; M. E. Hernandes; M. F.H. Iglesias

doi:10.1007/978-3-319-73639-6_11

On the factorization of the polar of a plane branch

A. Hefez, M. E. Hernandes, M. F.H. Iglesias

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Irreducible complex plane curve germs with the same characteristic exponents form an equisingularity class. In this paper we determine the Zariski invariants that characterize the general polar of a general member of such an equisingularity class. More precisely, we will describe explicitly the characteristic exponents of the irreducible components of the polar and their mutual intersection multiplicities, allowing us in particular to describe completely the content of each of Merle’s packages of the polar.

Original language	English
Title of host publication	Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3
Editors	Jawad Snoussi, Raimundo Nonato Araujo dos Santos, Marcelo J. Saia, David Mond, Aurelio Menegon Neto
Publisher	Springer New York LLC
Pages	347-362
Number of pages	16
ISBN (Print)	9783319736389
DOIs	https://doi.org/10.1007/978-3-319-73639-6_11
State	Published - 2018
Externally published	Yes
Event	2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015 - Salvador, Brazil Duration: 13 Jul 2015 → 17 Jul 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	222
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015
Country/Territory	Brazil
City	Salvador
Period	13/07/15 → 17/07/15

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

Keywords

Equisingularity
Polar curves
Polar decomposition

Access to Document

10.1007/978-3-319-73639-6_11

Cite this

Hefez, A., Hernandes, M. E., & Iglesias, M. F. H. (2018). On the factorization of the polar of a plane branch. In J. Snoussi, R. N. Araujo dos Santos, M. J. Saia, D. Mond, & A. Menegon Neto (Eds.), Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3 (pp. 347-362). (Springer Proceedings in Mathematics and Statistics; Vol. 222). Springer New York LLC. https://doi.org/10.1007/978-3-319-73639-6_11

Hefez, A. ; Hernandes, M. E. ; Iglesias, M. F.H. / On the factorization of the polar of a plane branch. Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. editor / Jawad Snoussi ; Raimundo Nonato Araujo dos Santos ; Marcelo J. Saia ; David Mond ; Aurelio Menegon Neto. Springer New York LLC, 2018. pp. 347-362 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{319b7a63eb554273b08ed88599d89128,

title = "On the factorization of the polar of a plane branch",

abstract = "Irreducible complex plane curve germs with the same characteristic exponents form an equisingularity class. In this paper we determine the Zariski invariants that characterize the general polar of a general member of such an equisingularity class. More precisely, we will describe explicitly the characteristic exponents of the irreducible components of the polar and their mutual intersection multiplicities, allowing us in particular to describe completely the content of each of Merle{\textquoteright}s packages of the polar.",

keywords = "Equisingularity, Polar curves, Polar decomposition",

author = "A. Hefez and Hernandes, {M. E.} and Iglesias, {M. F.H.}",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG, part of Springer Nature 2018.; 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015 ; Conference date: 13-07-2015 Through 17-07-2015",

year = "2018",

doi = "10.1007/978-3-319-73639-6_11",

language = "Ingl{\'e}s",

isbn = "9783319736389",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer New York LLC",

pages = "347--362",

editor = "Jawad Snoussi and {Araujo dos Santos}, {Raimundo Nonato} and Saia, {Marcelo J.} and David Mond and {Menegon Neto}, Aurelio",

booktitle = "Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3",

}

Hefez, A, Hernandes, ME & Iglesias, MFH 2018, On the factorization of the polar of a plane branch. in J Snoussi, RN Araujo dos Santos, MJ Saia, D Mond & A Menegon Neto (eds), Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. Springer Proceedings in Mathematics and Statistics, vol. 222, Springer New York LLC, pp. 347-362, 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015, Salvador, Brazil, 13/07/15. https://doi.org/10.1007/978-3-319-73639-6_11

On the factorization of the polar of a plane branch. / Hefez, A.; Hernandes, M. E.; Iglesias, M. F.H.
Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. ed. / Jawad Snoussi; Raimundo Nonato Araujo dos Santos; Marcelo J. Saia; David Mond; Aurelio Menegon Neto. Springer New York LLC, 2018. p. 347-362 (Springer Proceedings in Mathematics and Statistics; Vol. 222).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - On the factorization of the polar of a plane branch

AU - Hefez, A.

AU - Hernandes, M. E.

AU - Iglesias, M. F.H.

N1 - Publisher Copyright: © Springer International Publishing AG, part of Springer Nature 2018.

PY - 2018

Y1 - 2018

N2 - Irreducible complex plane curve germs with the same characteristic exponents form an equisingularity class. In this paper we determine the Zariski invariants that characterize the general polar of a general member of such an equisingularity class. More precisely, we will describe explicitly the characteristic exponents of the irreducible components of the polar and their mutual intersection multiplicities, allowing us in particular to describe completely the content of each of Merle’s packages of the polar.

AB - Irreducible complex plane curve germs with the same characteristic exponents form an equisingularity class. In this paper we determine the Zariski invariants that characterize the general polar of a general member of such an equisingularity class. More precisely, we will describe explicitly the characteristic exponents of the irreducible components of the polar and their mutual intersection multiplicities, allowing us in particular to describe completely the content of each of Merle’s packages of the polar.

KW - Equisingularity

KW - Polar curves

KW - Polar decomposition

UR - http://www.scopus.com/inward/record.url?scp=85044474248&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-73639-6_11

DO - 10.1007/978-3-319-73639-6_11

M3 - Contribución a la conferencia

AN - SCOPUS:85044474248

SN - 9783319736389

T3 - Springer Proceedings in Mathematics and Statistics

SP - 347

EP - 362

BT - Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3

A2 - Snoussi, Jawad

A2 - Araujo dos Santos, Raimundo Nonato

A2 - Saia, Marcelo J.

A2 - Mond, David

A2 - Menegon Neto, Aurelio

PB - Springer New York LLC

T2 - 2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015

Y2 - 13 July 2015 through 17 July 2015

ER -

Hefez A, Hernandes ME, Iglesias MFH. On the factorization of the polar of a plane branch. In Snoussi J, Araujo dos Santos RN, Saia MJ, Mond D, Menegon Neto A, editors, Singularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3. Springer New York LLC. 2018. p. 347-362. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-319-73639-6_11

On the factorization of the polar of a plane branch

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this