The Euclidean distance degree of smooth complex projective varieties
Copyright policy )The Euclidean distance degree of smooth complex projective varieties
We obtain several formulas for the Euclidean distance degree (ED degree) of an arbitrary nonsingular variety in projective space: in terms of Chern and Segre classes, Milnor classes, Chern-Schwartz-MacPherson classes, and an extremely simple formula equating the Euclidean distance degree of X with the Euler characteristic of an open subset of X.
- Max Planck Institute for Mathematics Germany
- Max Planck Institute for Mathematics in the Sciences Germany
- Max Planck Society Germany
- Florida State University United States
- Florida Southern College United States
14C17, algebraic optimization, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Chern–Schwartz–MacPherson classes, Real algebraic sets, intersection theory, Mathematics - Algebraic Geometry, Chern-Schwartz-MacPherson classes, Enumerative problems (combinatorial problems) in algebraic geometry, Characteristic classes and numbers in differential topology, 57R20, FOS: Mathematics, 14N10, characteristic classes, Algebraic Geometry (math.AG)
14C17, algebraic optimization, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Chern–Schwartz–MacPherson classes, Real algebraic sets, intersection theory, Mathematics - Algebraic Geometry, Chern-Schwartz-MacPherson classes, Enumerative problems (combinatorial problems) in algebraic geometry, Characteristic classes and numbers in differential topology, 57R20, FOS: Mathematics, 14N10, characteristic classes, Algebraic Geometry (math.AG)
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