Smoothness and irreducibility of varieties of plane curves with nodes and cusps

Eugenii Shustin

Bulletin de la Société Mathématique de France (1994)

  • Volume: 122, Issue: 2, page 235-253
  • ISSN: 0037-9484

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Shustin, Eugenii. "Smoothness and irreducibility of varieties of plane curves with nodes and cusps." Bulletin de la Société Mathématique de France 122.2 (1994): 235-253. <http://eudml.org/doc/87689>.

@article{Shustin1994,
author = {Shustin, Eugenii},
journal = {Bulletin de la Société Mathématique de France},
keywords = {irreducible curves; degree; nodes; cusps},
language = {eng},
number = {2},
pages = {235-253},
publisher = {Société mathématique de France},
title = {Smoothness and irreducibility of varieties of plane curves with nodes and cusps},
url = {http://eudml.org/doc/87689},
volume = {122},
year = {1994},
}

TY - JOUR
AU - Shustin, Eugenii
TI - Smoothness and irreducibility of varieties of plane curves with nodes and cusps
JO - Bulletin de la Société Mathématique de France
PY - 1994
PB - Société mathématique de France
VL - 122
IS - 2
SP - 235
EP - 253
LA - eng
KW - irreducible curves; degree; nodes; cusps
UR - http://eudml.org/doc/87689
ER -

References

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  1. [1] GREUEL (G.-M.) and KARRAS (U.). — Families of varieties with prescribed singularities, Compositio Math., t. 69 (1), 1989, p. 83-110. Zbl0684.32015MR90d:32037
  2. [2] HARRIS (J.). — On the Severi problem, Invent. Math., t. 84, 1985, p. 445-461. Zbl0596.14017MR87f:14012
  3. [3] HARTSHORNE (R.). — Algebraic geometry. — New York, Springer, 1977. Zbl0367.14001MR57 #3116
  4. [4] HIRSCHOWITZ (A.). — Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques, J. Reine Angew. Math., t. 397, 1989, p. 208-213. Zbl0686.14013MR90g:14021
  5. [5] HIRZEBRUCH (F.). — Singularities of algebraic surface and characteristic numbers, Contemp. Math., t. 58, 1986, p. 141-155. Zbl0601.14030MR87j:14057
  6. [6] IVINSKIS (K.). — Normale Flächen und die Miyaoka-Kobayashi Ungleichung. — Diplomarbeit, Bonn, 1985. 
  7. [7] KANG (P.-L.). — On the variety of plane curves of degree d with δ nodes and k cusps, Trans. Amer. Math. Soc., t. 316 (1), 1989, p. 165-192. Zbl0702.14019MR90g:14014
  8. [9] KANG (P.-L.). — A note on the variety of plane curves with nodes and cusps, Proc. Amer. Math. Soc., t. 106 (2), 1989, p. 309-312. Zbl0702.14020MR89k:14046
  9. [9] SEVERI (F.). — Vorlesungen über algebraische Geometrie (Anhang F). — Leipzig, Teubner, 1921. JFM48.0687.01
  10. [10] SHUSTIN (E.). — Smoothness and irreducibility of varieties of plane singular curves, Arithmetic and geometry of varieties, Kuibyshev, Kuibyshev Univ. Press, 1989, p. 132-145 (Russian). Zbl0767.14010
  11. [11] SHUSTIN (E.). — Geometry of discriminant and topology of algebraic curves, Proc. Intern. Congress Math., Kyoto, Aug. 21-29, 1990, vol. 1, Kyoto, 1991, p. 559-567. Zbl0802.14013
  12. [12] SHUSTIN (E.). — On manifolds of singular algebraic curves, Selecta Math. Soviet., t. 10 (1), 1991, p. 27-37. Zbl0804.14011MR1099434
  13. [13] SHUSTIN (E.). — Real plane algebraic curves with prescribed singularities, Topology, t. 32 (4), 1993, p. 845-856. Zbl0845.14017MR95f:14049
  14. [14] VAN DER WAERDEN (B.L.). — Einführung in die algebraische Geometrie. — 2nd ed., Berlin, Springer, 1973. Zbl0264.14001
  15. [15] ZARISKI (O.). — Algebraic surfaces. — 2nd ed., Heidelberg, Springer, 1971. Zbl0219.14020MR57 #9695

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