English

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

Algebraic Geometry 2020-04-02 v4 Commutative Algebra Category Theory

Abstract

The ideal transform of a graded module MM is known to compute the module of twisted global sections of the sheafification of MM 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

Cite

@article{arxiv.1409.6100,
  title  = {A constructive approach to the module of twisted global sections on relative projective spaces},
  author = {Mohamed Barakat and Markus Lange-Hegermann},
  journal= {arXiv preprint arXiv:1409.6100},
  year   = {2020}
}

Comments

Changed title, added examples, simplified arguments