AIM-ALGEBRAIC_GEOMETRY-0185 · Complete scoped theorem

Base-Divisor Degree Formulas for Two-View Algebraic Curves

Manuscript 23 October 2026 · Online 23 October 2026

math.AGUnrefereed preprint

Abstract

Let two fixed projective cameras with distinct centers have integral plane image curves of degrees m and n, neither an epipolar line, over an algebraically closed field of characteristic zero. We describe all integral reconstructions using the normalized components of the fiber product of the moving epipolar pencils. If a component has pencil degree h and pulled-back epipolar base divisors B_X and B_Y, its triangulated world curve has degree h + deg max(B_X, B_Y). This retains singular branches and images passing through the epipoles. We derive the total residual degree and an explicit formula for the baseline cycle multiplicity in terms of branch base orders and pencil ramification indices. When both moving pencils have degree one, the compatible integral world curve is unique, and the possible degrees for fixed m and n are exactly max(m,n), ..., m+n-1. The classical fiber-product method and twisted-cubic example are credited; the formulas here make their base-divisor corrections explicit. This is a complete scoped theorem related to AIM's fixed-camera compatibility question, not a claim to resolve every interpretation of that question. The preprint is unrefereed and makes no absolute priority claim.

Record

Affiliation
Mercury Software GmbH
Result
Complete scoped theorem
Categories
math.AG
Manuscript
23 October 2026
Online release
23 October 2026
Version
1.0
License
Creative Commons Attribution 4.0 International

Files and verification

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Citation

Alper Ferudun, “Base-Divisor Degree Formulas for Two-View Algebraic Curves,” EulerSolve Research Papers, AIM-ALGEBRAIC_GEOMETRY-0185, 2026. https://doi.org/10.5281/zenodo.23604002.

BibTeX
@misc{ferudun2026epipolardegrees,
  author = {Ferudun, Alper},
  title = {Base-Divisor Degree Formulas for Two-View Algebraic Curves},
  year = {2026},
  howpublished = {EulerSolve Research Papers},
  url = {https://eulersolve.org/papers/aim-algebraic-geometry-0185/},
  doi = {10.5281/zenodo.23604002},
  note = {AIM-ALGEBRAIC_GEOMETRY-0185; unrefereed preprint}
}

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