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Hodge diamond for Quot_C^n(E), E of rank R

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pbelmans committed Jul 8, 2019
1 parent aa0b051 commit 40fd20837ccf52f015a95aa27f0c5544438ae118
Showing with 15 additions and 0 deletions.
  1. +15 −0 diamond.sage
@@ -692,6 +692,21 @@ def moduli_vector_bundles(r, d, g):
return HodgeDiamond.from_polynomial(R(sum([one(C, g) * two(C, g) * three(C, g) * four(C, d, g) for C in Compositions(r)])), from_variety=True)


def quot_scheme_curve(g, n, r):
"""
Hodge diamond for the Quot scheme of zero-dimensional quotients of length ``r`` of a vector bundle of rank ``r`` on a curve of genus ``g``
For the proof, see proposition 4.5 of [1907.00826] (or rather, the reference [Bif89] in there)
* [1907.00826] Bagnarol--Fantechi--Perroni, On the motive of zero-dimensional Quot schemes on a curve
"""
def dn(P):
# shift in indexing because we start at 0
return sum([i * ni for (i, ni) in enumerate(P)])

return sum([product([symmetric_power(ni, g) for ni in P])(dn(P)) for P in IntegerVectors(n, r)])


def hilbtwo(X):
"""
Hodge diamond for the Hilbert square of any smooth projective variety

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