Algebraic geometry
On a family of complex algebraic surfaces of degree 3n
Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 699-702.

We study a class of algebraic surfaces of degree 3n in the complex projective space with only ordinary double points. They are obtained by using bivariate polynomials with complex coefficients related to the generalized cosine associated with the affine Weyl group of the root system A2.

Nous étudions une classe de surfaces algébriques de degré 3n dans ĺespace projectif complexe, avec seulement des points doubles ordinaires. Ils sont générés par des polynômes complexes qui sont liés au cosinus généralisé associé au groupe de Weyl affine du système de racines A2.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.09.009
Escudero, Juan García 1

1 Universidad de Oviedo, Facultad de Ciencias, 33007 Oviedo, Spain
@article{CRMATH_2013__351_17-18_699_0,
     author = {Escudero, Juan Garc{\'\i}a},
     title = {On a family of complex algebraic surfaces of degree 3\protect\emph{n}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {699--702},
     publisher = {Elsevier},
     volume = {351},
     number = {17-18},
     year = {2013},
     doi = {10.1016/j.crma.2013.09.009},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2013.09.009/}
}
TY  - JOUR
AU  - Escudero, Juan García
TI  - On a family of complex algebraic surfaces of degree 3n
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 699
EP  - 702
VL  - 351
IS  - 17-18
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2013.09.009/
DO  - 10.1016/j.crma.2013.09.009
LA  - en
ID  - CRMATH_2013__351_17-18_699_0
ER  - 
%0 Journal Article
%A Escudero, Juan García
%T On a family of complex algebraic surfaces of degree 3n
%J Comptes Rendus. Mathématique
%D 2013
%P 699-702
%V 351
%N 17-18
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.09.009/
%R 10.1016/j.crma.2013.09.009
%G en
%F CRMATH_2013__351_17-18_699_0
Escudero, Juan García. On a family of complex algebraic surfaces of degree 3n. Comptes Rendus. Mathématique, Volume 351 (2013) no. 17-18, pp. 699-702. doi : 10.1016/j.crma.2013.09.009. http://www.numdam.org/articles/10.1016/j.crma.2013.09.009/

[1] Breske, S.; Labs, O.; van Straten, D. Real line arrangements and surfaces with many real nodes (Jüttler, B.; Piene, R., eds.), Geometric Modeling and Algebraic Geometry, Springer, Berlin, 2008, pp. 47-54

[2] Chmutov, S.V. Examples of projective surfaces with many singularities, J. Algebr. Geom., Volume 1 (1992), pp. 191-196

[3] Escudero, J.G. Random tilings of spherical 3-manifolds, J. Geom. Phys., Volume 58 (2008), pp. 1451-1464

[4] Escudero, J.G. A construction of algebraic surfaces with many real nodes, 2011 | arXiv

[5] Escudero, J.G. Hypersurfaces with many Aj-singularities: Explicit constructions, J. Comput. Appl. Math. (2013) (in press) | DOI

[6] Hoffman, M.E.; Withers, D. Generalized Chebyshev polynomials associated with affine Weyl groups, Trans. Amer. Math. Soc., Volume 282 (1988), pp. 555-575

[7] Withers, D. Folding polynomials and their dynamics, Amer. Math. Monthly, Volume 95 (1988), pp. 399-413

Cited by Sources: