Framed sheaves on projective space and Quot schemes
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AbstractWe prove that, given integers $$m\ge 3$$ m ≥ 3 , $$r\ge 1$$ r ≥ 1 and $$n\ge 0$$ n ≥ 0 , the moduli space of torsion free sheaves on $${\mathbb {P}}^m$$ P m with Chern character $$(r,0,\ldots ,0,-n)$$ ( r , 0 , … , 0 , - n ) that are trivial along a hyperplane $$D \subset {\mathbb {P}}^m$$ D ⊂ P m is isomorphic to the Quot scheme $$\mathrm{Quot}_{{\mathbb {A}}^m}({\mathscr {O}}^{\oplus r},n)$$ Quot A m ( O ⊕ r , n ) of 0-dimensional length n quotients of the free sheaf $${\mathscr {O}}^{\oplus r}$$ O ⊕ r on $${\mathbb {A}}^m$$ A m . The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.
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2018 ◽
Vol 2020
(23)
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pp. 9011-9074
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1998 ◽
Vol 09
(04)
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pp. 513-522
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2002 ◽
Vol 13
(10)
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pp. 1117-1151
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2011 ◽
Vol 147
(5)
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pp. 1479-1518
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