Real enumerative invariants relative to the toric boundary and their refinement

We introduce new invariants of a class of toric surfaces (including the projective plane) that arise from appropriate enumeration of real curves of genus 1 and 2. These invariants admit a refinement similar to the one introduced by Grigory Mikhalkin in the rational case.

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Publication Details

Journal
Algebraic geometry
Published
2026-10-28
DOI
https://doi.org/10.14231/ag-2026-024
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

Real enumerative invariants relative to the toric boundary and their refinement

Eugenii I. Shustin, Ilia Itenberg
1 links
Algebraic geometry
Algebraic Geometry and Number Theory
article

Real enumerative invariants relative to the toric boundary and their refinement

Eugenii I. Shustin, Ilia Itenberg
article en

Abstract

We introduce new invariants of a class of toric surfaces (including the projective plane) that arise from appropriate enumeration of real curves of genus 1 and 2. These invariants admit a refinement similar to the one introduced by Grigory Mikhalkin in the rational case.

Algebraic geometry
Openalex Percentile: Top 96%
Algebraic Geometry and Number Theory
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Real enumerative invariants relative to the toric boundary and their refinement — Eugenii I. Shustin, Ilia Itenberg · Algebraic geometry (2026) | TGRS Research Map | TGRS