Counting twisted Higgs bundles

Motivic classes of the moduli spaces of twisted Higgs bundles

For more details see arXiv:1104.5698 and arXiv:1901.02439.


sage: from msinvar.higgs_bundles import CurveAlgebra
sage: from msinvar.higgs_bundles import twisted_higgs_bundles_invariant as invar
sage: C=CurveAlgebra(g=2)
sage: invar(C,l=2,r=2).factor()
(y - 1)^4 * y^10 * (y^2 + 1) * (y^4 - 4*y + 2)
class msinvar.higgs_bundles.CurveAlgebra(g=0, vars='y')[source]

Bases: msinvar.rings.RationalFunctionField

The algebra where zeta function of a curve lives.

For simplicity we define the algebra to be Q(y,t) or Q(u,v,t). In the first case the zeta function is (1-y*t)^(2*g)/(1-t)/(1-y^2*t)


Zeta function of a curve. It has the form (1-y*t)^(2*g)/(1-t)/(1-y^2*t).

H(part, p)[source]

Compute the function H from arXiv:1104.5698 (7).

msinvar.higgs_bundles.twisted_higgs_bundles_invariant(C, l, r)[source]

Invariants of the moduli space of l-twisted rank r Higgs bundles over a curve C.

Expected dimension of the moduli space is 1+l*r^2. For l=2g-2 it is 2+l*r^2. The final power twist is given by arXiv:1901.02439 (6).