# zbMATH — the first resource for mathematics

The degree of a Severi variety. (English) Zbl 0629.14020
Let $$P_ d$$ be the projective space that parametrizes all curves in $$P_ 2$$ of fixed degree d. The author gives a recursive procedure which enables one to calculate the degree in $$P_ d$$ of a Severi variety of curves with a fixed number of nodes and no other singularities.
Reviewer: A.Papantonopoulou

##### MSC:
 14H10 Families, moduli of curves (algebraic) 14M99 Special varieties 14N05 Projective techniques in algebraic geometry
##### Keywords:
degree; Severi variety
Full Text:
##### References:
 [1] F. Enriques, Sui moduli d’una classe di superficie e sul teorema d’esistenza per funzioni algebriche di due variabili, Atti Accad. Sci. Torino 47 (1912). · JFM 43.0709.01 [2] William Fulton, On nodal curves, Algebraic geometry — open problems (Ravello, 1982) Lecture Notes in Math., vol. 997, Springer, Berlin, 1983, pp. 146 – 155. · Zbl 0514.14012 [3] Joe Harris, On the Severi problem, Invent. Math. 84 (1986), no. 3, 445 – 461. · Zbl 0596.14017 [4] Ziv Ran, On nodal plane curves, Invent. Math. 86 (1986), no. 3, 529 – 534. · Zbl 0644.14009 [5] Z. Ran, The Severi problem: a post-mortem(?), Mathematical aspects of string theory (San Diego, Calif., 1986) Adv. Ser. Math. Phys., vol. 1, World Sci. Publishing, Singapore, 1987, pp. 394 – 407. [6] Z. Ran, Degeneration of linear systems (preprint). [7] F. Severi, Vorlesungen über Algebraische Geometrie, Teubner, Leipzig, 1921. · JFM 48.0687.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.