CoCalc Public FilesStrataclasses.ipynbOpen in with one click!
Author: Johannes Schmitt
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Description: Computing fundamental classes of strata of differentials using the package admcycles

Below we compute the divisor class given by the closure H21(2)M2,1\overline{\mathcal{H}}_2^1(2) \subset \overline{\mathcal{M}}_{2,1} of the locus H21(2)={(C,p): differential η on C with double zero at p}M2,1{\mathcal{H}}_2^1(2) = {\{(C,p) : \exists \text{ differential $\eta$ on $C$ with double zero at $p$} \}} \subset {\mathcal{M}}_{2,1} Execute the commands below by clicking and pressing Shift+Enter.

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from admcycles import * g=2; k=1; A=(2,); H = Strataclass(g,k,A); H.simplify()

We can check that it agrees with the locus of (hyperelliptic) curves with a marked Weierstrass point, which is computed by a different algorithm.

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(H-Hyperell(2,1)).is_zero()