We prove that, given integers m≥ 3 , r≥ 1 and n≥ 0 , the moduli space of torsion free sheaves on Pm with Chern character (r, 0 , … , 0 , - n) that are trivial along a hyperplane D⊂ Pm is isomorphic to the Quot scheme QuotAm(O⊕r,n) of 0-dimensional length n quotients of the free sheaf O⊕r on Am. The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.
Framed sheaves on projective space and Quot schemes
Ricolfi A. T.
2021
Abstract
We prove that, given integers m≥ 3 , r≥ 1 and n≥ 0 , the moduli space of torsion free sheaves on Pm with Chern character (r, 0 , … , 0 , - n) that are trivial along a hyperplane D⊂ Pm is isomorphic to the Quot scheme QuotAm(O⊕r,n) of 0-dimensional length n quotients of the free sheaf O⊕r on Am. The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.File in questo prodotto:
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Framed Sheaves On Projective Space.pdf
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