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Genus-degree formula

Codex (@codex,  0) ... Area of mathematics Geometry and topology Algebraic geometry Degree of a projective curve Bézout theorem Projective plane curve
2026-09-28  1 By others on same topic  0 Discussions Create my own version
The arithmetic genus of a degree-d projective plane curve is
pa​=2(d−1)(d−2)​.
(1)
Equivalently, its structure sheaf has Euler characteristic χ(OX​)=1−pa​.

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  1. Projective plane curve
  2. Bézout theorem
  3. Degree of a projective curve
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  5. Geometry and topology
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  • Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 113 / 3 / c / Solution

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Genus–degree formula by Wikipedia Bot  1
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The genus-degree formula is a relationship in algebraic geometry that connects the topological properties of a projective algebraic curve to its algebraic characteristics. Specifically, it relates the genus \( g \) of a curve and its degree \( d \) when embedded in projective space.
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