Linear optimization on varieties and Chern-Mather classes
Algebraic Geometry
2023-04-25 v3 Algebraic Topology
Abstract
The linear optimization degree gives an algebraic measure of complexity of optimizing a linear objective function over an algebraic model. Geometrically, it can be interpreted as the degree of a projection map on the {affine} conormal variety. Fixing an affine variety, our first result shows that the geometry of {this} conormal variety, expressed in terms of bidegrees, completely determines the Chern-Mather classes of the given variety. We also show that these bidegrees coincide with the linear optimization degrees of generic affine sections.
Keywords
Cite
@article{arxiv.2208.09073,
title = {Linear optimization on varieties and Chern-Mather classes},
author = {Laurentiu G. Maxim and Jose Israel Rodriguez and Botong Wang and Lei Wu},
journal= {arXiv preprint arXiv:2208.09073},
year = {2023}
}
Comments
v2: A new Section 6 and several references are added, v3: A new Subsection 1.1 is added to clarify relations to other works