Node polynomials for families: methods and applications

DOI10.1002/mana.200310182zbMath1066.14063arXivmath/0111299OpenAlexW2133654688MaRDI QIDQ4812392

Ragni Piene, Steven Lawrence Kleiman

Publication date: 20 August 2004

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0111299

zbMATH Keywords

Hilbert schemeBell polynomialnodal curvequintic threefoldGöttsche's conjectureEnriques diagramabelian surfac

Mathematics Subject Classification ID

Enumerative problems (combinatorial problems) in algebraic geometry (14N10)

Related Items (18)

The Kleiman-Piene conjecture and node polynomials for plane curves in \(\mathbb{P}^3\) ⋮ Polynomiality properties of tropical refined invariants ⋮ Severi degrees on toric surfaces ⋮ Node polynomials for curves on surfaces ⋮ A short proof of the Göttsche conjecture ⋮ Enumeration of cones with singular base ⋮ Enumeration of rational curves in a moving family of \(\mathbb{P}^2\) ⋮ Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I ⋮ THE DI FRANCESCO–ITZYKSON–GÖTTSCHE CONJECTURES FOR NODE POLYNOMIALS OF ℙ² ⋮ Enriques diagrams, arbitrarily near points, and Hilbert schemes ⋮ Computing Severi degrees with long-edge graphs ⋮ Rational cuspidal curves on del-Pezzo surfaces ⋮ Counting planar curves in \(\mathbb{P}^3\) with degenerate singularities ⋮ Enumeration of singular algebraic curves ⋮ Relative node polynomials for plane curves ⋮ Rational cuspidal curves in a moving family of \(\mathbb{P}^2\) ⋮ Rational Curves of Degree 10 on a General Quintic Threefold ⋮ On the universal scheme of r-relative clusters of a family

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