The Euclidean distance degree of smooth complex projective varieties

被引：15

作者：

Aluffi, Paolo ^{[1
]}

Harris, Corey ^{[2
]}

机构：

[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

[2] Max Planck Inst Math Sci, Leipzig, Germany

来源：

ALGEBRA & NUMBER THEORY | 2018年 / 12卷 / 08期

关键词：

algebraic optimization; intersection theory; characteristic classes; Chern-Schwartz-MacPherson classes; CHERN CLASSES;

D O I：

10.2140/ant.2018.12.2005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：2005 / 2032

页数：28

共 29 条

[1] Computing characteristic classes of projective schemes [J].

Aluffi, P .

JOURNAL OF SYMBOLIC COMPUTATION, 2003, 35 (01) :3-19

[2]

Aluffi P, 2000, ADV STU P M, V29, P1

[3] Differential forms with logarithmic poles and Chern-Schwartz-MacPherson classes of singular varieties [J].

Aluffi, P .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (07) :619-624

[4] Singular schemes of hypersurfaces [J].

Aluffi, P .

DUKE MATHEMATICAL JOURNAL, 1995, 80 (02) :325-351

[5] Chern classes for singular hypersurfaces [J].

Aluffi, P .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 351 (10) :3989-4026

[6]

Aluffi P., 1994, International Mathematics Research Notices, V1994, P455

[7] PROJECTIVE DUALITY AND A CHERN-MATHER INVOLUTION [J].

Aluffi, Paolo .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 370 (03) :1803-1822

[8] Tensored Segre classes [J].

Aluffi, Paolo .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2017, 221 (06) :1366-1382

[9] Euler characteristics of general linear sections and polynomial Chern classes [J].

Aluffi P. .

Rendiconti del Circolo Matematico di Palermo, 2013, 62 (1) :3-26

[10]

[Anonymous], MACAULAY2 SOFTWARE S

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