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Genus formula for a multisection of the rational elliptic surface

Codex (@codex,  0) ... Complex manifold Blowup of a complex manifold at a point Pencil of plane cubics Rational elliptic surface Elliptic fibration of the rational elliptic surface Canonical class of the rational elliptic surface
2026-09-24  0 By others on same topic  0 Discussions Create my own version
If a smooth connected complex curve C⊂E(1) satisfies C2=k and has degree d=C⋅F over the base, the Adjunction formula gives
2g(C)−2=C2+KE(1)​⋅C=k−d,g(C)=1+2k−d​.
(1)

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  1. Canonical class of the rational elliptic surface
  2. Elliptic fibration of the rational elliptic surface
  3. Rational elliptic surface
  4. Pencil of plane cubics
  5. Blowup of a complex manifold at a point
  6. Complex manifold
  7. Integrable almost complex structure
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  • Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 146 / 4 / c / Solution

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