On the quantum cohomology of the plane, old and new, and a K3 analogue.

Z. Ran

Displaying similar documents to “On the quantum cohomology of the plane, old and new, and a K3 analogue.”

Halphen gaps and good space curves

Jan O. Kleppe (1998)

Bollettino dell'Unione Matematica Italiana

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In questo articolo dimostriamo l'esistenza di curve "buone e generali" di grado $d$ e genere $g$ che giacciono su di una superfice liscia di grado $s$ , per ogni $s \geq 4$ , $d \geq (\begin{matrix} s \\ 2 \end{matrix})$ , e $g$ in un certo intervallo vicino al genere massimo.

Curves on a smooth quadric.

S. Giuffrida, R. Maggioni (2003)

Collectanea Mathematica

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We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines the curve.

Divisors on Mg,g+1 and the minimal resolution conjecture for points on canonical curves

Gavril Farkas, Mircea Mustaţǎ, Mihnea Popa (2003)

Annales scientifiques de l'École Normale Supérieure

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A souped-up version of Pardini's theorem and its application to funny curves

Masaaki Homma (1989)

Compositio Mathematica

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Enumerative geometry of divisorial families of rational curves

Ziv Ran (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We compute the number of irreducible rational curves of given degree with 1 tacnode in $¶^{2}$ or 1 node in $¶^{3}$ meeting an appropriate generic collection of points and lines. As a byproduct, we also compute the number of rational plane curves of degree $d$ passing through $3 d - 2$ given points and tangent to a given line. The method is ‘classical’, free of Quantum Cohomology.

On the finiteness of rational curves on quintic threefolds

Sheldon Katz (1986)

Compositio Mathematica

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