A Constructive Approach to the Module of Twisted Global Sections on Relative Projective Spaces

Mohamed Barakat () and Markus Lange-Hegermann ()
Additional contact information
Mohamed Barakat: University of Siegen
Markus Lange-Hegermann: RWTH Aachen University, Lehrstuhl B für Mathematik

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 23-49 from Springer

Abstract: Abstract The ideal transform of a graded module M is known to compute the module of twisted global sections of the sheafification of M over a relative projective space. We introduce a second description motivated by the relative BGG-correspondence. However, our approach avoids the full BGG-correspondence by replacing the Tate resolution with the computationally more efficient purely linear saturation and the Castelnuovo-Mumford regularity with the often enough much smaller linear regularity. This paper provides elementary, constructive, and unified proofs that these two descriptions compute the (truncated) modules of twisted global sections. The main argument relies on an established characterization of Gabriel monads.

Keywords: Serre quotient category; Reflective localization of Abelian categories; Gabriel monad; (Truncated) Module of twisted global sections; Direct image functor; Linear regularity; Gröbner bases; Saturation; 13D02; 13D07; 13D45; 13P10; 13P20; 18E10; 18E35; 18A40; 68W30; 14Q99 (search for similar items in EconPapers)
Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_2

Ordering information: This item can be ordered from
http://www.springer.com/9783319705668

DOI: 10.1007/978-3-319-70566-8_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().