Dessins d'enfants for analysts

Vincent Beffara

Pré-Publication, Document De Travail Année : 2015

Dessins d'enfants for analysts

(1)

Vincent Beffara

Fonction : Auteur
PersonId : 3387
IdHAL : vincent-beffara
ORCID : 0000-0002-6928-318X
IdRef : 080234577

Unité de Mathématiques Pures et Appliquées

Résumé

We present an algorithmic way of exactly computing Belyi functions for hypermaps and triangulations in genus $0$ or $1$, and the associated dessins, based on a numerical iterative approach initialized from a circle packing combined with subsequent lattice reduction. The main advantage compared to previous methods is that it is applicable to much larger graphs; we use very little algebraic geometry, and aim for this paper to be as self-contained as possible.

Mots clés

Riemann surface Belyi function Dessin d'enfant

Domaines

Variables complexes [math.CV] Géométrie algébrique [math.AG]

Fichier principal

Belyi_analysts.pdf (2.55 Mo)

Belyi_analysts.bbl (3 Ko)

fig/dessin_random_1.png (134.96 Ko)

fig/dessin_random_2.png (114.58 Ko)

fig/ex1/2 (2.22 Ko)

fig/ex1/3 (11.39 Ko)

fig/ex1/4 (87.77 Ko)

fig/ex1/s1/i1_map.pdf (5.35 Ko)

fig/ex1/s1/i1_pic.png (24.3 Ko)

fig/ex1/s2/i1_map.pdf (9.02 Ko)

fig/ex1/s2/i1_pic.png (28.71 Ko)

fig/ex1/s2/i2_map.pdf (7.86 Ko)

fig/ex1/s2/i2_pic.png (26.8 Ko)

fig/ex1/s2/i3_map.pdf (10.66 Ko)

fig/ex1/s2/i3_pic.png (36.28 Ko)

fig/ex1/s3/i10_map.pdf (16.33 Ko)

fig/ex1/s3/i10_pic.png (44.88 Ko)

fig/ex1/s3/i11_map.pdf (13.52 Ko)

fig/ex1/s3/i11_pic.png (35.76 Ko)

fig/ex1/s3/i1_map.pdf (13.26 Ko)

fig/ex1/s3/i1_pic.png (36.3 Ko)

fig/ex1/s3/i2_map.pdf (14.52 Ko)

fig/ex1/s3/i2_pic.png (41.53 Ko)

fig/ex1/s3/i3_map.pdf (11.12 Ko)

fig/ex1/s3/i3_pic.png (29.94 Ko)

fig/ex1/s3/i4_map.pdf (11.93 Ko)

fig/ex1/s3/i4_pic.png (39.29 Ko)

fig/ex1/s3/i5_map.pdf (12.04 Ko)

fig/ex1/s3/i5_pic.png (37.78 Ko)

fig/ex1/s3/i6_map.pdf (14.53 Ko)

fig/ex1/s3/i6_pic.png (47.42 Ko)

fig/ex1/s3/i7_map.pdf (10.81 Ko)

fig/ex1/s3/i7_pic.png (33.1 Ko)

fig/ex1/s3/i8_map.pdf (11.8 Ko)

fig/ex1/s3/i8_pic.png (34.38 Ko)

fig/ex1/s3/i9_map.pdf (11.3 Ko)

fig/ex1/s3/i9_pic.png (36.36 Ko)

fig/ex1/s4/i10_map.pdf (17.93 Ko)

fig/ex1/s4/i10_pic.png (46.31 Ko)

fig/ex1/s4/i11_map.pdf (20.7 Ko)

fig/ex1/s4/i11_pic.png (43.89 Ko)

fig/ex1/s4/i12_map.pdf (19.32 Ko)

fig/ex1/s4/i12_pic.png (40.82 Ko)

fig/ex1/s4/i13_map.pdf (16.75 Ko)

fig/ex1/s4/i13_pic.png (38.96 Ko)

fig/ex1/s4/i14_map.pdf (18.91 Ko)

fig/ex1/s4/i14_pic.png (42.61 Ko)

fig/ex1/s4/i15_map.pdf (19.5 Ko)

fig/ex1/s4/i15_pic.png (43.37 Ko)

fig/ex1/s4/i16_map.pdf (14.81 Ko)

fig/ex1/s4/i16_pic.png (40.92 Ko)

fig/ex1/s4/i17_map.pdf (15.46 Ko)

fig/ex1/s4/i17_pic.png (35.11 Ko)

fig/ex1/s4/i18_map.pdf (17.17 Ko)

fig/ex1/s4/i18_pic.png (42.11 Ko)

fig/ex1/s4/i19_map.pdf (18.25 Ko)

fig/ex1/s4/i19_pic.png (42.19 Ko)

fig/ex1/s4/i1_map.pdf (18.52 Ko)

fig/ex1/s4/i1_pic.png (33.51 Ko)

fig/ex1/s4/i20_map.pdf (21.07 Ko)

fig/ex1/s4/i20_pic.png (47.53 Ko)

fig/ex1/s4/i21_map.pdf (13.19 Ko)

fig/ex1/s4/i21_pic.png (36.73 Ko)

fig/ex1/s4/i22_map.pdf (17.14 Ko)

fig/ex1/s4/i23_map.pdf (19.98 Ko)

fig/ex1/s4/i24_map.pdf (22.65 Ko)

fig/ex1/s4/i25_map.pdf (19.38 Ko)

fig/ex1/s4/i26_map.pdf (13.71 Ko)

fig/ex1/s4/i27_map.pdf (19.54 Ko)

fig/ex1/s4/i28_map.pdf (22.19 Ko)

fig/ex1/s4/i29_map.pdf (19.04 Ko)

fig/ex1/s4/i2_map.pdf (16.28 Ko)

fig/ex1/s4/i30_map.pdf (16.75 Ko)

fig/ex1/s4/i31_map.pdf (15.71 Ko)

fig/ex1/s4/i32_map.pdf (15.18 Ko)

fig/ex1/s4/i33_map.pdf (21.97 Ko)

fig/ex1/s4/i34_map.pdf (21.99 Ko)

fig/ex1/s4/i35_map.pdf (16.17 Ko)

fig/ex1/s4/i36_map.pdf (16.14 Ko)

fig/ex1/s4/i37_map.pdf (15.23 Ko)

fig/ex1/s4/i38_map.pdf (16.33 Ko)

fig/ex1/s4/i39_map.pdf (21.79 Ko)

fig/ex1/s4/i3_map.pdf (16.36 Ko)

fig/ex1/s4/i40_map.pdf (14.81 Ko)

fig/ex1/s4/i41_map.pdf (16.23 Ko)

fig/ex1/s4/i42_map.pdf (19.91 Ko)

fig/ex1/s4/i43_map.pdf (13.11 Ko)

fig/ex1/s4/i43_pic.png (40.62 Ko)

fig/ex1/s4/i44_map.pdf (18.23 Ko)

fig/ex1/s4/i44_pic.png (32.98 Ko)

fig/ex1/s4/i45_map.pdf (14.57 Ko)

fig/ex1/s4/i45_pic.png (36.18 Ko)

fig/ex1/s4/i46_map.pdf (15.17 Ko)

fig/ex1/s4/i46_pic.png (43.2 Ko)

fig/ex1/s4/i47_map.pdf (15.78 Ko)

fig/ex1/s4/i47_pic.png (36.99 Ko)

fig/ex1/s4/i48_map.pdf (17.12 Ko)

fig/ex1/s4/i48_pic.png (43.69 Ko)

fig/ex1/s4/i49_map.pdf (13.57 Ko)

fig/ex1/s4/i49_pic.png (37.97 Ko)

fig/ex1/s4/i4_map.pdf (15.02 Ko)

fig/ex1/s4/i4_pic.png (43.19 Ko)

fig/ex1/s4/i50_map.pdf (15.76 Ko)

fig/ex1/s4/i50_pic.png (44.04 Ko)

fig/ex1/s4/i51_map.pdf (104.03 Ko)

fig/ex1/s4/i51_pic.png (41.4 Ko)

fig/ex1/s4/i52_map.pdf (15.27 Ko)

fig/ex1/s4/i52_pic.png (45.41 Ko)

fig/ex1/s4/i53_map.pdf (15.58 Ko)

fig/ex1/s4/i53_pic.png (43.39 Ko)

fig/ex1/s4/i54_map.pdf (16.48 Ko)

fig/ex1/s4/i54_pic.png (37.38 Ko)

fig/ex1/s4/i55_map.pdf (15.08 Ko)

fig/ex1/s4/i55_pic.png (36.45 Ko)

fig/ex1/s4/i56_map.pdf (17.96 Ko)

fig/ex1/s4/i56_pic.png (43.03 Ko)

fig/ex1/s4/i57_map.pdf (15.05 Ko)

fig/ex1/s4/i57_pic.png (32.87 Ko)

fig/ex1/s4/i58_map.pdf (15.26 Ko)

fig/ex1/s4/i58_pic.png (39.9 Ko)

fig/ex1/s4/i59_map.pdf (18.79 Ko)

fig/ex1/s4/i59_pic.png (44.83 Ko)

fig/ex1/s4/i5_map.pdf (15.64 Ko)

fig/ex1/s4/i5_pic.png (48.46 Ko)

fig/ex1/s4/i60_map.pdf (14.8 Ko)

fig/ex1/s4/i60_pic.png (44.53 Ko)

fig/ex1/s4/i61_map.pdf (18.87 Ko)

fig/ex1/s4/i61_pic.png (52.23 Ko)

fig/ex1/s4/i62_map.pdf (13.87 Ko)

fig/ex1/s4/i62_pic.png (37.06 Ko)

fig/ex1/s4/i63_map.pdf (15.33 Ko)

fig/ex1/s4/i63_pic.png (38.21 Ko)

fig/ex1/s4/i64_map.pdf (17.24 Ko)

fig/ex1/s4/i64_pic.png (41.41 Ko)

fig/ex1/s4/i6_map.pdf (19.54 Ko)

fig/ex1/s4/i6_pic.png (47.04 Ko)

fig/ex1/s4/i7_map.pdf (16.68 Ko)

fig/ex1/s4/i7_pic.png (43.11 Ko)

fig/ex1/s4/i8_map.pdf (15.51 Ko)

fig/ex1/s4/i8_pic.png (46.69 Ko)

fig/ex1/s4/i9_map.pdf (15.28 Ko)

fig/ex1/s4/i9_pic.png (38.34 Ko)

fig/map.pdf (3.12 Ko)

fig/map_b.pdf (3.42 Ko)

fig/map_h.pdf (13.36 Ko)

fig/map_t.pdf (4.42 Ko)

fig/subdivision.pdf (3.04 Ko)

fig/subdivision_n.pdf (3.78 Ko)