Cuspidal curves on Hirzebruch surfaces

[1]  S. Iitaka.  Complex Analysis and Algebraic Geometry: On Logarithmic Kodaira Dimension of Algebraic Varieties , 1977 .

[2]  T. Matsuoka,et al.  The degree of rational cuspidal curves , 1989 .

[3]  Eduardo Casas-Alvero,et al.  Singularities of plane curves , 2000 .

[4]  William Fulton,et al.  Introduction to Toric Varieties. (AM-131) , 1993 .

[5]  H. G. Telling,et al.  The Rational Quartic Curve in Space of Three and Four Dimensions: Being An Introduction To Rational Curves , 1936 .

[6]  M. Nagata.  On rational surfaces I. Irreducible curves of arithmetic genus $0$ or $1$ , 1960 .

[7]  Rational Cuspidal Plane Curves of Type (d,d — 3) , 1997, alg-geom/9709001.

[8]  Duality of real projective plane curves: Klein's equation , 1996 .

[9]  On a new class of rational cuspidal plane curves with two cusps , 2012, 1205.1248.

[10]  Torgunn Karoline Moe.  Rational Cuspidal Curves , 2015, 1511.02691.

[11]  Lucien Szpiro,et al.  Liaison des variétés algébriques. I , 1974 .

[12]  K. Tono.  On the number of the cusps of cuspidal plane curves , 2005 .

[13]  A. Clebsch.  Ueber diejenigen ebenen Curven, deren Coordinaten rationale Functionen eines Parameters sind. , 1865 .

[14]  Solomon Lefschetz.  On the existence of loci with given singularities , 1913 .

[15]  M. Namba,et al.  Geometry of Projective Algebraic Curves , 1984 .

[16]  Isao Wakabayashi.  On the logarithmic Kodaira dimension of the complement of a curve in $P^2$ , 1978 .

[17]  Francoise Pene,et al.  On the Degree of Caustics by Reflection , 2012, 1201.0621.

[18]  Antonio Laface.  On Linear Systems of Curves on Rational Scrolls , 2002 .

[19]  Diane Maclagan,et al.  Multigraded Castelnuovo-Mumford Regularity , 2003 .

[20]  Joe Harris,et al.  Counting plane curves of any genus , 1996, alg-geom/9608025.

[21]  Julius Plucker.  Theorie der algebraischen Curven : gegründet auf eine neue Behandlungsweise der analytischen Geometrie , 1839 .

[22]  M. Miyanishi,et al.  On a projective plane curve whose complement has logarithmic Kodaira dimension , 1981 .

[23]  On Orevkov's rational cuspidal plane curves , 2009, 0909.2554.

[24]  Ragni Piene,et al.  Cuspidal projections of space curves , 1981 .

[25]  Jun Li,et al.  Universal polynomials for singular curves on surfaces , 2012, Compositio Mathematica.

[26]  Y. Miyaoka.  The maximal number of quotient singularities on surfaces with given numerical invariants , 1984 .

[27]  David A. Cox.  The homogeneous coordinate ring of a toric variety , 2013 .

[28]  Yu-jong Tzeng.  A proof of the Göttsche-Yau-Zaslow formula , 2010, 1009.5371.

[29]  S. Orevkov.  On rational cuspidal curves , 2002 .

[30]  H. Hilton.  Plane algebraic curves , 1921 .

[31]  F. Sakai,et al.  Rational cuspidal curves of type $(d,d-2)$ with one or two cusps , 2000 .

[32]  J. Coolidge.  A Treatise on Algebraic Plane Curves , 1959 .

[33]  A. Némethi,et al.  On rational cuspidal plane curves, open surfaces and local singularities , 2007 .

[34]  V. Danilov,et al.  THE GEOMETRY OF TORIC VARIETIES , 1978 .

[35]  Paolo Aluffi.  Computing characteristic classes of projective schemes , 2003, J. Symb. Comput..

[36]  C. Wall.  Highly singular quintic curves , 1996, Mathematical Proceedings of the Cambridge Philosophical Society.

[37]  L. Göttsche.  A Conjectural Generating Function for Numbers of Curves on Surfaces , 1997, alg-geom/9711012.

[38]  A. Némethi,et al.  On rational cuspidal curves, open surfaces and local singularities , 2006, math/0604421.

[39]  R. Vakil.  Counting curves on rational surfaces , 2000 .

[40]  E. Ballico.  CUSPIDAL CURVES ON THE SMOOTH QUADRIC SURFACE , 2011 .

[41]  Jens Piontkowski,et al.  On the Number of Cusps of Rational Cuspidal Plane Curves , 2007, Exp. Math..

[42]  K. Tono.  Defining equations¶of certain rational cuspidal curves. I , 2000 .

[43]  R. Kobayashi,et al.  A numerical characterization of ball quotients for normal surfaces with branch loci , 1989 .

[44]  On a class of rational cuspidal plane curves , 1995, alg-geom/9507004.

[45]  On the number of singular points of plane curves , 1995, alg-geom/9507005.

[46]  M. Miyanishi,et al.  Non-complete algebraic surfaces with logarithmic Kodaira dimension - ∞ and with non-connected boundaries at infinity , 1984 .

[47]  T. Fujita.  On the topology of non-complete algebraic surfaces , 1982 .

[48]  Hisao Yoshihara,et al.  On plane rational curves , 1979 .

[49]  J. Stillwell,et al.  Plane Algebraic Curves , 1986 .

[50]  Karol Palka.  The Coolidge-Nagata conjecture holds for curves with more than four cusps , 2012, 1202.3491.

[51]  Arthur Cayley,et al.  A Treatise on the Higher Plane Curves: Intended as a Sequel to a Treatise on Conic Sections , 2001 .

[52]  Theorie der ebenen algebraischen Kurven hoherer Ordnung , 1906 .