On rational surfaces I. Irreducible curves of arithmetic genus $0$ or $1$

  title={On rational surfaces I. Irreducible curves of arithmetic genus \$0\$ or \$1\$},
  author={M. Nagata},
The Coolidge-Nagata conjecture, part I
Let E⊆P2 be a complex rational cuspidal curve contained in the projective plane and let (X,D)→(P2,E) be the minimal log resolution of singularities. Applying the log Minimal Model Program to (X,12D)Expand
Maximal Quasiprojective Subsets and the Kleiman-Chevalley Quasiprojectivity Criterion
We prove that any complete Q-factorial variety con- tains only finitely many maximal open quasiprojective subsets. Let X be a normal variety defined over an algebraically closed field of anyExpand
Heegaard Floer Homologies and Rational Cuspidal Curves. Lecture notes
This is an expanded version of the lecture course the second author gave at Winterbraids VI in Lille in February 2016.
Dynamical degrees of birational transformations of projective surfaces
The dynamical degree lambda( f )  of a birational transformation f measures the exponential growth rate of the degree of the formulae that define the n -th iterate of f  . We study the set of allExpand
On Rational Cuspidal Projective Plane Curves
In 2002, L. Nicolaescu and the fourth author formulated a very general conjecture which relates the geometric genus of a Gorenstein surface singularity with rational homology sphere link with theExpand
10E9 solution to the elliptic Painlevé equation Dedicated to Professor Kyoichi Takano on his sixtieth birthday
A τ function formalism for Sakai’s elliptic Painlevé equation is presented. This establishes the equivalence between the two formulations by Sakai and by Ohta-Ramani-Grammaticos. We also give aExpand
Heegaard Floer homology and plane curves with non-cuspidal singularities
We study possible configurations of singular points occuring on general algebraic curves in CP 2 via Floer theory. To achieve this, we describe a general formula for the H1-action on the knot FloerExpand
On the extendability of projective varieties: a survey
We give a survey of the incredibly beautiful amount of geometry involved with the problem of realizing a projective variety as hyperplane section of another variety.
The minimal Cremona degree of quartic surfaces
Two birational projective varieties in Pn are Cremona Equivalent if there is a birational modification of Pn mapping one onto the other. The minimal Cremona degree of X ⊂ Pn is the minimal integerExpand