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## GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn

#### Michael Lönne [1]

##### 85 165

We consider naturally generated subgroups En of Brn. On the geometric side we show that En is the bifurcation braid monodromy group of the family of plane polynomial coverings of degree 3. On the algebraic side there is the Hurwitz action of the braid group Brn on the n-fold Cartesian product Brn3 of Br3 = ha, b | aba = babi. The stabiliser of finite alternating sequences of its generators a, b is expected to be given by En. We are able to prove this conjecture in a few cases and apply our results to give characterisations in the most basic instances of the paths realised by degenerations in families of polynomials as defined by Donaldson.
braid group, Hurwitz action, braid monodromy
Konular JA48AP26FJ Makaleler Yazar: Michael Lönne
 Bibtex @ { ieja266425, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2010}, volume = {8}, pages = {1 - 17}, doi = {}, title = {GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn}, key = {cite}, author = {Lönne, Michael} } APA Lönne, M . (2010). GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn. International Electronic Journal of Algebra, 8 (8), 1-17. Retrieved from http://dergipark.gov.tr/ieja/issue/25212/266425 MLA Lönne, M . "GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn". International Electronic Journal of Algebra 8 (2010): 1-17 Chicago Lönne, M . "GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn". International Electronic Journal of Algebra 8 (2010): 1-17 RIS TY - JOUR T1 - GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn AU - Michael Lönne Y1 - 2010 PY - 2010 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 1 EP - 17 VL - 8 IS - 8 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn %A Michael Lönne %T GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn %D 2010 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 8 %N 8 %R %U ISNAD Lönne, Michael . "GEOMETRIC AND ALGEBRAIC SIGNIFICANCE OF SOME HURWITZ STABILISERS IN Brn". International Electronic Journal of Algebra 8 / 8 (Aralık 2010): 1-17.