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PreprintCC BY 4.0arXiv

On elements of degree g in the separating semigroup of a real curve of genus g

  • G. B. Mikhalkin
  • S. Yu. Orevkov
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Abstract

Let C be a separating real algebraic curve of genus g whose real locus consists of r components and let S=Sep(C) be its separating semigroup. An element δ∈ S is called extendable if δ+ℕ0r⊂ S, where ℕ0={n∈ℤ| n≥ 0}. We prove that an element of S is extendable if it is realizable by a separating mobile divisor of degree g and projective rank 1.

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Cite

BibTeXRIS
BibTeX
@misc{mikhalkin2026elements,
  title = {{On elements of degree $g$ in the separating semigroup of a real curve of genus $g$}},
  author = {G. B. Mikhalkin and S. Yu. Orevkov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25483},
  eprint = {2610.25483},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25483},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On elements of degree g in the separating semigroup of a real curve of genus g
AU  - G. B. Mikhalkin
AU  - S. Yu. Orevkov
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25483
UR  - https://arxiv.org/abs/2610.25483
AB  - Let C be a separating real algebraic curve of genus g whose real locus consists of r components and let S=Sep(C) be its separating semigroup. An element δ∈ S is called extendable if δ+ℕ_0^r⊂ S, where ℕ_0={n∈ℤ| n≥ 0}. We prove that an element of S is extendable if it is realizable by a separating mobile divisor of degree g and projective rank 1.
ER  -