Enumeration of genus-three plane curves with a fixed complex structure

DOI10.1090/S1056-3911-04-00375-3zbMath1070.14054arXivmath/0203058MaRDI QIDQ4659671

Aleksey Zinger

Publication date: 21 March 2005

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203058

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35)

Related Items (5)

Counting rational curves of arbitrary shape in projective spaces ⋮ Enumerative geometry of elliptic curves on toric surfaces ⋮ Equivariant degenerations of plane curve orbits ⋮ Rational cuspidal curves on del-Pezzo surfaces ⋮ Rational cuspidal curves in a moving family of \(\mathbb{P}^2\)

Cites Work

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• Arnold conjecture and Gromov-Witten invariant
• Gromov-Witten classes, quantum cohomology, and enumerative geometry
• Genus \(1\) enumerative invariants in \(\mathbb{P}^n\) with fixed \(j\) invariant
• Linear orbits of smooth plane curves
• Intersections of ℚ-divisors on Kontsevich’s moduli space \overline{𝕄}_{0,𝕟}(ℙ^{𝕣},𝕕) and enumerative geometry
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Counting elliptic plane curves with fixed $j$-invariant
• Completion of Katz-Qin-Ruan's enumeration of genus-two plane curves
• Linear orbits of arbitrary plane curves.
• A mathematical theory of quantum cohomology

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