Counting curves on irrational surfaces
نویسندگان
چکیده
منابع مشابه
Counting Curves on Rational Surfaces
In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points). We rephrase their arguments in the language of maps, and extend them to other rational surfaces, and other specified intersections with a divisor. As applications, (i) we count irreducible curves on Hirzebruc...
متن کاملCounting Curves on Toric Surfaces
A few years ago, Tzeng settled a remarkable conjecture of Goettsche on counting nodal curves on smooth surfaces, proving that the formulas are given by certain universal polynomials. At the same time, Ardila and Block used the tropical approach of Brugalle, Mihalkin and Fomin to count nodal curves on a certain class of (not necessarily smooth) toric surfaces, and obtained similar polynomiality ...
متن کاملCounting Real Rational Curves on K3 Surfaces
We provide a real analog of the Yau-Zaslow formula counting rational curves on K3 surfaces. ”But man is a fickle and disreputable creature and perhaps, like a chess-player, is interested in the process of attaining his goal rather than the goal itself.” Fyodor Dostoyevsky, Notes from the Underground.
متن کاملCounting Elliptic Curves in K3 Surfaces
We compute the genus g = 1 family GW-invariants of K3 surfaces for non-primitive classes. These calculations verify Göttsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships among various generating functions. The number of genus g curves in K3 surfaces X repr...
متن کاملCounting Generic Genus–0 Curves on Hirzebruch Surfaces
Hirzebruch surfaces Fk provide an excellent example to underline the fact that in general symplectic manifolds, Gromov–Witten invariants might well count curves in the boundary components of the moduli spaces. We use this example to explain in detail that the counting argument given by Batyrev in [Bat93] for toric manifolds does not work (also see [Sie99, Proposition 4.6]).
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ژورنال
عنوان ژورنال: Surveys in Differential Geometry
سال: 1999
ISSN: 1052-9233,2164-4713
DOI: 10.4310/sdg.1999.v5.n1.a3