We prove that for any r > 1 the moduli space of stable Ulrich bundles of rank r and determinant O_X(r) on any smooth Fano threefold X of index two is smooth of dimension r^2 + 1 and that the same holds true for even r when the index is four, in which case no odd–rank Ulrich bundles exist. In particular this shows that any such threefold is Ulrich wild. As a preliminary result, we give necessary and sufficient conditions for the existence of Ulrich bundles on any smooth projective threefold in terms of the existence of a curve in the threefold enjoying special properties.

Ciliberto, C., Flamini, F., Knutsen Andreas, L. (2023). Ulrich bundles on Del Pezzo threefolds. JOURNAL OF ALGEBRA, 634, 209-236 [10.1016/j.jalgebra.2023.06.034].

Ulrich bundles on Del Pezzo threefolds

Ciliberto Ciro
Membro del Collaboration Group
;
Flamini Flaminio
Membro del Collaboration Group
;
2023-07-27

Abstract

We prove that for any r > 1 the moduli space of stable Ulrich bundles of rank r and determinant O_X(r) on any smooth Fano threefold X of index two is smooth of dimension r^2 + 1 and that the same holds true for even r when the index is four, in which case no odd–rank Ulrich bundles exist. In particular this shows that any such threefold is Ulrich wild. As a preliminary result, we give necessary and sufficient conditions for the existence of Ulrich bundles on any smooth projective threefold in terms of the existence of a curve in the threefold enjoying special properties.
27-lug-2023
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Ulrich bundles; Fano 3folds; Moduli spaces
Ciliberto, C., Flamini, F., Knutsen Andreas, L. (2023). Ulrich bundles on Del Pezzo threefolds. JOURNAL OF ALGEBRA, 634, 209-236 [10.1016/j.jalgebra.2023.06.034].
Ciliberto, C; Flamini, F; Knutsen Andreas, L
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
Ulrich_JAlg_2023.pdf

solo utenti autorizzati

Descrizione: Articolo Principale
Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 542.78 kB
Formato Adobe PDF
542.78 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/300147
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact