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RandomCanonicalCurves :: canonicalCurve

canonicalCurve -- Compute a random canonical curve of genus less or equal to 14

Synopsis

Description

Compute a random canonical curve of genus $g \le{} 14$, based on the proofs of unirationality of $M_g$ by Severi, Sernesi, Chang-Ran and Verra.

i1 : setRandomSeed "alpha";
i2 : g=14;
i3 : FF=ZZ/10007;
i4 : R=FF[x_0..x_(g-1)];
i5 : time betti(I=(random canonicalCurve)(g,R))
     -- used 5.98479 seconds

            0  1
o5 = total: 1 66
         0: 1  .
         1: . 66

o5 : BettiTally
i6 : genus I == g and degree I ==2*g-2

o6 = true

For the programmer

The object canonicalCurve is an instance of the type RandomObject.