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Conjecture B for X10 and its genus-two mirror

  • Alex Junior Gomez Saltachin
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Abstract

We prove Conjecture B of Akhtar--Coates--Corti--Heuberger--Kasprzyk--Oneto--Petracci--Prince--Tveiten unconditionally for the normalized family of maximally mutable Laurent polynomials with prescribed T-binomial edge coefficients associated with the degree-10 orbifold del Pezzo hypersurface X10⊂ℙ(1,2,3,5). An explicit S-extended quantum-period calculation determines the affine mirror map λ=a−346 and proves that the regularized quantum period equals the classical period as a formal power series throughout the family.

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Cite

BibTeXRIS
BibTeX
@misc{saltachin2026conjecture,
  title = {{Conjecture B for $X_10$ and its genus-two mirror}},
  author = {Alex Junior Gomez Saltachin},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04293},
  eprint = {2611.04293},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04293},
}
RIS
TY  - UNPB
TI  - Conjecture B for X_10 and its genus-two mirror
AU  - Alex Junior Gomez Saltachin
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04293
UR  - https://arxiv.org/abs/2611.04293
AB  - We prove Conjecture B of Akhtar--Coates--Corti--Heuberger--Kasprzyk--Oneto--Petracci--Prince--Tveiten unconditionally for the normalized family of maximally mutable Laurent polynomials with prescribed T-binomial edge coefficients associated with the degree-10 orbifold del Pezzo hypersurface X_10⊂ℙ(1,2,3,5). An explicit S-extended quantum-period calculation determines the affine mirror map λ=a−346 and proves that the regularized quantum period equals the classical period as a formal power series throughout the family.
ER  -