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.
Cazzaniga A., Ricolfi A.T. (2022). Framed sheaves on projective space and Quot schemes. MATHEMATISCHE ZEITSCHRIFT, 300(1), 745-760 [10.1007/s00209-021-02802-x].
Framed sheaves on projective space and Quot schemes
Ricolfi A. T.
2022
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:
| File | Dimensione | Formato | |
|---|---|---|---|
|
Framed Sheaves On Projective Space.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione (CCBY)
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.
