Abstract
Let V (d, m, k) be the variety of plane projective irreducible curves of degree d with m nodes and k cusps as their only singularities. We prove that V (d, m, k) is non-empty, non-singular and irreducible when m + 2k < αd2, where α is some absolute explicit constant. This estimate is optimal with respect to the exponent of d
Original language | English |
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Pages (from-to) | 235-253 |
Number of pages | 19 |
Journal | Bulletin de la Societe Mathematique de France |
Volume | 122 |
Issue number | 2 |
DOIs | |
State | Published - 1994 |
Keywords
- FAMILY OF SINGULAR PLANE ALGEBRAIC CURVES
- LINEAR SYSTEM
- RIEMANN-ROCH THEOREM
- IRREDUCIBILITY