scholarly journals Freeness and invariants of rational plane curves

2019 ◽  
Vol 89 (323) ◽  
pp. 1525-1546
Author(s):  
Laurent Busé ◽  
Alexandru Dimca ◽  
Gabriel Sticlaru
Keyword(s):  
Plane Curves ◽  
Rational Plane

scholarly journals A new method to compute the singularities of offsets to rational plane curves

2015 ◽  
Vol 290 ◽  
pp. 385-402 ◽  
Author(s):  
Juan Gerardo Alcázar ◽  
Jorge Caravantes ◽  
Gema M. Diaz-Toca
Keyword(s):  
New Method ◽  
Plane Curves ◽  
Rational Plane

Bend, break and count II: elliptics, cuspidals, linear genera

1999 ◽  
Vol 127 (1) ◽  
pp. 7-12
Author(s):  
Z. RAN
Keyword(s):  
Ruled Surfaces ◽  
Plane Curves ◽  
Recursive Procedure ◽  
Rational Plane ◽  
Tangent Direction

In [R2] we showed how elementary considerations involving geometry on ruled surfaces may be used to obtain recursive enumerative formulae for rational plane curves. Here we show how similar considerations may be used to obtain further enumerative formulae, as follow. First some notation. As usual we denote by Ngd the number of irreducible plane curves of degree d and genus g through 3d+g−1 general points. Also, we denote by Ngd→ (resp. Ngd×) the number of such curves passing through general points A1, …, A3d+g−2 and having a given tangent direction (resp. a node) at A1. As is well known and easy to see, we haveformula hereFor any d, g, these numbers are computed in [R1] as part of a more general recursive procedure. For N0d, N1d, relatively simple recursions have been given by Kontsevich–Manin (see [FP]) and Eguchi–Hori–Xiong–Getzler (see [P1]), respectively.

scholarly journals Rational plane curves parameterizable by conics

2013 ◽  
Vol 373 ◽  
pp. 453-480 ◽  
Author(s):  
Teresa Cortadellas Benítez ◽  
Carlos DʼAndrea
Keyword(s):  
Plane Curves ◽  
Rational Plane

scholarly journals Counting rational plane curves

2000 ◽  
Vol 72 (4) ◽  
pp. 610-610
Author(s):  
Israel Vainsencher
Keyword(s):  
Plane Curves ◽  
Rational Plane
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