期刊
ADVANCES IN MATHEMATICS
卷 437, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2023.109443
关键词
Segre classes; Polar degrees; Linear optimization degree; Local Euler obstruction; Chern-Mather classes; Conormal varieties
类别
The paper investigates the relationship between linear optimization degree and geometric structure. By analyzing the geometric structure of the conormal variety of an affine variety, the Chern-Mather classes of the given variety can be completely determined. Additionally, the paper shows that these bidegrees coincide with the linear optimization degrees of generic affine sections.
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.(c) 2023 Elsevier Inc. All rights reserved.
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