Residues for maps generically transverse to distributions

Câmara, Leonardo; Corrêa, Maurício

doi:10.1090/proc/14198

Residues for maps generically transverse to distributions
HTML articles powered by AMS MathViewer

by Leonardo M. Câmara and Maurício Corrêa PDF

Proc. Amer. Math. Soc. 146 (2018), 5225-5234 Request permission

Abstract:

We show a residues formula for maps generically transversal to regular holomorphic distributions.

References

Arnaud Beauville, Fano contact manifolds and nilpotent orbits, Comment. Math. Helv. 73 (1998), no. 4, 566–583. MR 1639888, DOI 10.1007/s000140050069
Filippo Bracci and Bruno Scárdua, Holomorphic vector fields transverse to polydiscs, J. Lond. Math. Soc. (2) 75 (2007), no. 1, 99–115. MR 2302732, DOI 10.1112/jlms/jdl005
Jean-Paul Brasselet, Une généralisation de la formule de Riemann-Hurwitz, Journées de géométrie analytique (Univ. Poitiers, Poitiers, 1972), Bull. Soc. Math. France Suppl. Mém., No. 38, Soc. Math. France, Paris, 1974, pp. 99–106 (French). MR 0361176, DOI 10.24033/msmf.157
Jean-Paul Brasselet, Sur une formule de M. H. Schwartz relative aux revêtements ramifiés, C. R. Acad. Sci. Paris Sér. A-B 283 (1976), no. 2, Ai, A41–A44 (French, with English summary). MR 419818
Marco Brunella, Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. École Norm. Sup. (4) 30 (1997), no. 5, 569–594 (French, with English and French summaries). MR 1474805, DOI 10.1016/S0012-9593(97)89932-6
Maurício Corrêa Jr. and Márcio G. Soares, A Poincaré type inequality for one-dimensional multiprojective foliations, Bull. Braz. Math. Soc. (N.S.) 42 (2011), no. 3, 485–503. MR 2833814, DOI 10.1007/s00574-011-0026-3
El Hadji Cheikh Mbacké Diop, Résidus d’applications holomorphes entre variétés, Hokkaido Math. J. 29 (2000), no. 1, 171–200 (French, with English summary). MR 1745509, DOI 10.14492/hokmj/1350912963
William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620, DOI 10.1007/978-3-662-02421-8
Tomoaki Honda, A localization lemma and its applications, Sūrikaisekikenkyūsho K\B{o}kyūroku 1033 (1998), 110–118. Singularities and complex analytic geometry (Japanese) (Kyoto, 1997). MR 1660634
Tomoaki Honda, Tangential index of foliations with curves on surfaces, Hokkaido Math. J. 33 (2004), no. 2, 255–273. MR 2072998, DOI 10.14492/hokmj/1285766165
Birger Iversen, Critical points of an algebraic function, Invent. Math. 12 (1971), 210–224. MR 342512, DOI 10.1007/BF01418781
Toshikazu Ito and Bruno Scárdua, On the classification of non-integrable complex distributions, Indag. Math. (N.S.) 17 (2006), no. 3, 397–406. MR 2321108, DOI 10.1016/S0019-3577(06)80040-6
Takeshi Izawa, Residues for non-transversality of a holomorphic map to a codimension one holomorphic foliation, J. Math. Soc. Japan 59 (2007), no. 3, 899–910. MR 2344833
Takeshi Izawa and Tatsuo Suwa, Multiplicity of functions of singular varieties, Internat. J. Math. 14 (2003), no. 5, 541–558. MR 1993796, DOI 10.1142/S0129167X03001910
Stefan Kebekus, Lines on contact manifolds, J. Reine Angew. Math. 539 (2001), 167–177. MR 1863858, DOI 10.1515/crll.2001.072
Stefan Kebekus, Lines on complex contact manifolds. II, Compos. Math. 141 (2005), no. 1, 227–252. MR 2099777, DOI 10.1112/S0010437X04000880
M.-H. Schwartz, Champs de repères tangents à une variété presque complexe, Bull. Soc. Math. Belg. 19 (1967), 389–420 (French). MR 243449