A tropical calculation of the Welschinger invariants of real toric Del Pezzo surfaces

DOI10.1090/S1056-3911-06-00434-6zbMath1118.14059arXivmath/0406099OpenAlexW1989560268MaRDI QIDQ5487961

Eugenii I. Shustin

Publication date: 13 September 2006

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

Full work available at URL: https://arxiv.org/abs/math/0406099

zbMATH Keywords

enumerative geometrytropical curvesWelschinger invariantsDel Pezzo surfaces

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Real algebraic sets (14P05) 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 (18)

Pencils of quadrics and Gromov-Witten-Welschinger invariants of \(\mathbb {CP}^3\) ⋮ New cases of logarithmic equivalence of Welschinger and Gromov-Witten invariants ⋮ Welschinger invariants of toric del Pezzo surfaces with nonstandard real structures ⋮ Enumerative Aspects of the Gross-Siebert Program ⋮ Refined broccoli invariants ⋮ Enumeration of rational curves with cross-ratio constraints ⋮ A note on tropical triangles in the plane ⋮ Invariant count of holomorphic disks in the cotangent bundles of the two-sphere and real projective plane ⋮ Broccoli curves and the tropical invariance of Welschinger numbers ⋮ Real log curves in toric varieties, tropical curves, and log Welschinger invariants ⋮ A remark on the Gromov-Witten-Welschinger invariants of \(\mathbb{C}P^3\# \overline{\mathbb{C}P}^{3_*}\) ⋮ Tropical curves in abelian surfaces II: Enumeration of curves in linear systems ⋮ An imaginary refined count for some real rational curves ⋮ Tropical vertex and real enumerative geometry ⋮ Real Gromov-Witten theory ⋮ Counting tropical rational curves with cross-ratio constraints ⋮ Tropical real Hurwitz numbers ⋮ Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry

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• On Specializations of Curves. I
• Ideals Associated to Deformations of Singular Plane Curves
• Welschinger invariant and enumeration of real plane rational curves
• Enumerative tropical algebraic geometry in ℝ²
• Logarithmic equivalence of Welschinger and Gromov-Witten invariants

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