We study the principal parts bundles PkOℙn(d) as homogeneous bundles and we describe their associated quiver representations. With this technique we show that if n ≥ 2 and 0 ≤ d < k then there exists an invariant decomposition PkOℙn(d) = Qk,d ⊕ (SdV ⊗ Oℙn) with Qk,d a stable homogeneous vector bundle. The decomposition properties of such bundles were previously known only for n = 1 or k ≤ d or d < 0. Moreover we show that the Taylor truncation maps H0PkOℙn(d)→H0PhOℙn(d), defined for any h ≤ k and any d, have maximal rank.

Principal parts bundles on projective spaces and quiver representations

Re, Riccardo
2012-01-01

Abstract

We study the principal parts bundles PkOℙn(d) as homogeneous bundles and we describe their associated quiver representations. With this technique we show that if n ≥ 2 and 0 ≤ d < k then there exists an invariant decomposition PkOℙn(d) = Qk,d ⊕ (SdV ⊗ Oℙn) with Qk,d a stable homogeneous vector bundle. The decomposition properties of such bundles were previously known only for n = 1 or k ≤ d or d < 0. Moreover we show that the Taylor truncation maps H0PkOℙn(d)→H0PhOℙn(d), defined for any h ≤ k and any d, have maximal rank.
2012
Principal parts; Projective space; Quiver representation; Stable; Vector bundle; Mathematics (all)
Re, Riccardo
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/11383/2067711
 Attenzione

L'Ateneo sottopone a validazione solo i file PDF allegati

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? ND
social impact