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Computing fundamental classes of strata of differentials using the package admcycles

Project: admcycles
Views: 227
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Kernel: SageMath 9.0

Below we compute the divisor class given by the closure H‾21(2)⊂M‾2,1\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 $\etaon on Cwithdoublezeroat with double zero at pParseError: KaTeX parse error: Expected 'EOF', got '}' at position 1: }̲ \}} \subset {\…$ Execute the commands below by clicking and pressing Shift+Enter.

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.

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