We study some spectral sequences associated with a locally free OX-module A which has a Lie algebroid structure. Here X is either a complex manifold or a regular scheme over an algebraically closed field k. One spectral sequence can be associated with A by choosing a global section V of A, and considering a Koszul complex with a differential given by inner product by V. This spectral sequence is shown to degenerate at the second page by using Deligne’s degeneracy criterion. Another spectral sequence we study arises when considering the Atiyah algebroid DE of a holomolorphic vector bundle E on a complex manifold. If V is a differential operator on E with scalar symbol, i.e, a global section of DE, we associate with the pair (E, V) a twisted Koszul complex. The first spectral sequence associated with this complex is known to degenerate at the first page in the untwisted (E= 0) case.

Koszul complexes and spectral sequences associated with Lie algebroids / Bruzzo, U.; Rubtsov, V. N.. - In: SÃO PAULO JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1982-6907. - 15:2(2021), pp. 495-504. [10.1007/s40863-020-00199-9]

Koszul complexes and spectral sequences associated with Lie algebroids

Bruzzo, U.
Membro del Collaboration group
;
2021

Abstract

We study some spectral sequences associated with a locally free OX-module A which has a Lie algebroid structure. Here X is either a complex manifold or a regular scheme over an algebraically closed field k. One spectral sequence can be associated with A by choosing a global section V of A, and considering a Koszul complex with a differential given by inner product by V. This spectral sequence is shown to degenerate at the second page by using Deligne’s degeneracy criterion. Another spectral sequence we study arises when considering the Atiyah algebroid DE of a holomolorphic vector bundle E on a complex manifold. If V is a differential operator on E with scalar symbol, i.e, a global section of DE, we associate with the pair (E, V) a twisted Koszul complex. The first spectral sequence associated with this complex is known to degenerate at the first page in the untwisted (E= 0) case.
15
2
495
504
10.1007/s40863-020-00199-9
https://arxiv.org/abs/2012.09953
Bruzzo, U.; Rubtsov, V. N.
File in questo prodotto:
File Dimensione Formato  
Bruzzo-Rubtsov2020_Article_KoszulComplexesAndSpectralSequ copy.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 886.84 kB
Formato Adobe PDF
886.84 kB Adobe PDF Visualizza/Apri

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/20.500.11767/125837
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact