We prove that, given integers m >= 3, r >= 1 and n >= 0, themoduli space of torsion free sheaves on Pm with Chern character (r, 0 ,..., 0,-n) that are trivial along a hyperplane D subset of P-m is isomorphic to the Quot scheme Quot (m)(A) (O-circle plus r, n) of 0-dimensional length n quotients of the free sheaf O (circle plus r) on A(m). The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.
Framed sheaves on projective space and Quot schemes / Cazzaniga, Alberto; Ricolfi, Andrea T. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 300:1(2022), pp. 745-760. [10.1007/s00209-021-02802-x]
Framed sheaves on projective space and Quot schemes
Ricolfi, Andrea T
2022-01-01
Abstract
We prove that, given integers m >= 3, r >= 1 and n >= 0, themoduli space of torsion free sheaves on Pm with Chern character (r, 0 ,..., 0,-n) that are trivial along a hyperplane D subset of P-m is isomorphic to the Quot scheme Quot (m)(A) (O-circle plus r, n) of 0-dimensional length n quotients of the free sheaf O (circle plus r) on A(m). The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.| File | Dimensione | Formato | |
|---|---|---|---|
|
16. Framed Sheaves On Projective Space and Quot schemes.pdf
accesso aperto
Licenza:
Creative commons
Dimensione
370.42 kB
Formato
Adobe PDF
|
370.42 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
