@article{SIGMA_2018_14_a30,
author = {Susan Jane Colley and Gary Kennedy},
title = {Cartan {Prolongation} of a {Family} of {Curves} {Acquiring} a {Node}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2018},
volume = {14},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a30/}
}
Susan Jane Colley; Gary Kennedy. Cartan Prolongation of a Family of Curves Acquiring a Node. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a30/
[1] Brieskorn E., Knörrer H., Plane algebraic curves, Modern Birkhäuser Classics, Birkhäuser/Springer Basel AG, Basel, 1986 | DOI | MR
[2] Bryant R. L., “Nine lectures on exterior differential systems”, Graduate Summer Workshop on Exterior Differential Systems at the Mathematical Sciences Research Institute (1999) https://services.math.duke.edu/b̃ryant/MSRI_Lectures.pdf | MR
[3] Bryant R. L., Hsu L., “Rigidity of integral curves of rank $2$ distributions”, Invent. Math., 114 (1993), 435–461 | DOI | MR
[4] Cartan E., “Sur l'équivalence absolue de certains systèmes d'équations différentielles et sur certaines familles de courbes”, Bull. Soc. Math. France, 42 (1914), 12–48 | DOI | MR
[5] Castro A., Colley S. J., Kennedy G., Shanbrom C., “A coarse stratification of the monster tower”, Michigan Math. J., 66 (2017), 855–866, arXiv: 1606.07931 | DOI | MR
[6] Colley S. J., Kennedy G., “A higher-order contact formula for plane curves”, Comm. Algebra, 19 (1991), 479–508 | DOI | MR
[7] Colley S. J., Kennedy G., “Triple and quadruple contact of plane curves”, Enumerative Algebraic Geometry (Copenhagen, 1989), Contemp. Math., 123, Amer. Math. Soc., Providence, RI, 1991, 31–59 | DOI | MR
[8] Colley S. J., Kennedy G., “The enumeration of simultaneous higher-order contacts between plane curves”, Compositio Math., 93 (1994), 171–209, arXiv: alg-geom/9212003 | MR
[9] Gherardelli G., “Sul modello minimo della varietà degli elementi differenziali del $2^\circ$ ordine del piano projettivo”, Atti Accad. Italia. Rend. Cl. Sci. Fis. Mat. Nat. (7), 2 (1941), 821–828 | MR
[10] Giaro A., Kumpera A., Ruiz C., “Sur la lecture correcte d'un résultat d'Élie Cartan”, C. R. Acad. Sci. Paris Sér. A-B, 287 (1978), A241–A244 | MR
[11] Hartshorne R., Algebraic geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York–Heidelberg, 1977 | DOI | MR
[12] Kollár J., Lectures on resolution of singularities, Annals of Mathematics Studies, 166, Princeton University Press, Princeton, NJ, 2007 | MR
[13] Kumpera A., Ruiz C., “Sur l'équivalence locale des systèmes de Pfaff en drapeau”, Monge–Ampère Equations and Related Topics (Florence, 1980), Ist. Naz. Alta Mat. Francesco Severi, Rome, 1982, 201–248 | MR
[14] Lejeune-Jalabert M., “Chains of points in the Semple tower”, Amer. J. Math., 128 (2006), 1283–1311 | DOI | MR
[15] Montgomery R., Swaminathan V., Zhitomirskii M., “Resolving singularities with Cartan's prolongation”, J. Fixed Point Theory Appl., 3 (2008), 353–378 | DOI | MR
[16] Montgomery R., Zhitomirskii M., “Geometric approach to Goursat flags”, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18 (2001), 459–493 | DOI | MR
[17] Montgomery R., Zhitomirskii M., Points and curves in the Monster tower, Mem. Amer. Math. Soc., 203, 2010, x+137 pp. | DOI | MR
[18] Mormul P., “Exotic moduli of Goursat distributions exist already in codimension three”, Real and Complex Singularities, Contemp. Math., 459, Amer. Math. Soc., Providence, RI, 2008, 131–145 | DOI | MR
[19] Semple J. G., “Some investigations in the geometry of curve and surface elements”, Proc. London Math. Soc., 4 (1954), 24–49 | DOI | MR