- For example, one can use the arithmetic genus of the curve.
- These are surfaces fibred over a curve where the general fibre is a curve of arithmetic genus one with a cusp.
- In algebraic geometry, an "'elliptic singularity "'of a surface, introduced by, is a surface singularity such that the arithmetic genus of its local ring is 0.
- His method was to consider normal surfaces " Z " with a birational proper map to " Y " and show that there is a minimal one with minimal possible arithmetic genus.
- The irregularity then appeared as a new " correction " term measuring the difference " p " " g " & minus; " p " " a " of the geometric genus and the arithmetic genus of more complicated surfaces.