Piecewise linear sheaves
Algebraic Geometry
2019-06-04 v3
Abstract
On a finite-dimensional real vector space, we give a microlocal characterization of (derived) piecewise linear sheaves (PL sheaves) and prove that the triangulated category of such sheaves is generated by sheaves associated with convex polyhedra. We then give a similar theorem for PL gamma-sheaves, that is, PL sheaves associated with the gamma-topology, for a closed convex polyhedral proper cone gamma. Our motivation is that convex polyhedra may be considered as building blocks for higher dimensional barcodes.
Cite
@article{arxiv.1805.00349,
title = {Piecewise linear sheaves},
author = {Masaki Kashiwara and Pierre Schapira},
journal= {arXiv preprint arXiv:1805.00349},
year = {2019}
}
Comments
A few corrections, including bibliographical, with respect to the previous version. This paper is a continuation of arXiv:1705.00955. to appear at IMRN