Arkiv för Matematik

  • Ark. Mat.
  • Volume 54, Number 2 (2016), 277-297.

Euler sequence and Koszul complex of a module

Björn Andreas, Darío Sánchez Gómez, and Fernando Sancho de Salas

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Abstract

We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential p-forms of a projective bundle. In particular we generalize Bott’s formula for the projective space to a projective bundle over a scheme of characteristic zero.

Note

This work was supported by the SFB 647 ‘Space-Time-Matter:Arithmetic and Geometric Structures’ of the DFG (German Research Foundation) and by the Spanish grants MTM2013-45935-P (MINECO) and FS/12-2014 (Samuel Solórzano Barruso Foundation).

Article information

Source
Ark. Mat., Volume 54, Number 2 (2016), 277-297.

Dates
Received: 4 January 2016
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485802752

Digital Object Identifier
doi:10.1007/s11512-016-0236-4

Mathematical Reviews number (MathSciNet)
MR3546354

Zentralblatt MATH identifier
1373.13012

Rights
2016 © Institut Mittag-Leffler

Citation

Andreas, Björn; Sánchez Gómez, Darío; Sancho de Salas, Fernando. Euler sequence and Koszul complex of a module. Ark. Mat. 54 (2016), no. 2, 277--297. doi:10.1007/s11512-016-0236-4. https://projecteuclid.org/euclid.afm/1485802752


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