CoCalc Public FilesStrataclasses.ipynb
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 $\overline{\mathcal{H}}_2^1(2) \subset \overline{\mathcal{M}}_{2,1}$ of the locus ${\mathcal{H}}_2^1(2) = {\{(C,p) : \exists \text{ differential \eta on C with double zero at p} \}} \subset {\mathcal{M}}_{2,1}$ 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()