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Real enumerative invariants relative to the toric boundary and their refinement

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arxiv 2401.06718 v2 pith:MBGGO6I5 submitted 2024-01-12 math.AG

Ilia Itenberg , Eugenii Shustin This is my paper · ORCID
classification math.AG
keywords invariantsrealrefinementtoricadmitappropriateariseboundary
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We introduce new invariants of a class of toric surfaces (including the projective plane) that arise from appropriate enumeration of real curves of genus one and two. These invariants admit a refinement similar to the one introduced by Grigory Mikhalkin in the rational case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. BPS polynomials and Welschinger invariants

    math.AG 2025-06 conditional novelty 7.0 of 10

    The new BPS polynomials of surfaces specialize at q=-1 to Welschinger invariants for blowups of the projective plane at up to six points.

  2. Quantum index, Arnold-Rokhlin surfaces, and real enumerative geometry

    math.AG 2026-07 conditional novelty 6.0 of 10

    Two Welschinger-type sign rules for real curves on toric surfaces are the same up to a factor (−1)^(...) tied to degree, genus, and an Arnold-Rokhlin quantum index.

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