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genus(Ring) -- arithmetic genus

Synopsis

Usage:
genus R
Function: genus
Inputs:
- R, a ring
Outputs:
- an integer

Description

Computes the arithmetic genus of the projective scheme V with homogeneous coordinate ring R

i1 : R = QQ[x,y,z]/ideal(y^2*z-x^3)

o1 = R

o1 : QuotientRing

i2 : genus R

o2 = 1

See also

genera -- list of the successive linear sectional arithmetic genera
euler -- Euler characteristic