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In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer

A constructive approach to the module of twisted global sections on relative projective spaces

Mohamed Barakat und Markus Lange-Hegermann,
Mar 2018

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.

Literatur Beschaffung: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, Springer
@book{2361,
author= {Barakat, Mohamed and Lange-Hegermann, Markus},
title= {A constructive approach to the module of twisted global sections on relative projective spaces},
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.},
booktitle= {Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory},
year= {2018},
month= {Mar},
publisher= {Springer},
address= {https://arxiv.org/abs/1409.6100},
editor= {},
pages= {},
organisation= {},
}