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PreprintarXiv licencearXiv

On wall-crossing invariant combinations of Welschinger numbers for rational surfaces with a conic bundle

  • Sergey Finashin
  • Viatcheslav Kharlamov
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Abstract

We refine the real enumerative invariants insensitive to changes in the real structure introduced in our previous paper on del Pezzo surfaces, and extend these refined invariants to arbitrary rational surfaces. The construction involves a choice of an auxiliary conic bundle together with a Pin-structure. We prove that the resulting invariants are independent of these auxiliary choices and establish recursive relations for their computation.

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Cite

BibTeXRIS
BibTeX
@misc{finashin2026wallcrossing,
  title = {{On wall-crossing invariant combinations of Welschinger numbers for rational surfaces with a conic bundle}},
  author = {Sergey Finashin and Viatcheslav Kharlamov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02445},
  eprint = {2610.02445},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02445},
}
RIS
TY  - UNPB
TI  - On wall-crossing invariant combinations of Welschinger numbers for rational surfaces with a conic bundle
AU  - Sergey Finashin
AU  - Viatcheslav Kharlamov
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02445
UR  - https://arxiv.org/abs/2610.02445
AB  - We refine the real enumerative invariants insensitive to changes in the real structure introduced in our previous paper on del Pezzo surfaces, and extend these refined invariants to arbitrary rational surfaces. The construction involves a choice of an auxiliary conic bundle together with a Pin-structure. We prove that the resulting invariants are independent of these auxiliary choices and establish recursive relations for their computation.
ER  -