Vector bundles and regulous maps

被引：14

作者：

Bilski, Marcin ^{[1
]}

Kucharz, Wojciech ^{[1
]}

Valette, Anna ^{[1
]}

Valette, Guillaume ^{[2
]}

机构：

[1] Uniwersytetu Jagiellonskiego, Wydzial Matematyki & Informatyki, PL-30348 Krakow, Poland

[2] Inst Matematyczny PAN, PL-31027 Krakow, Poland

来源：

MATHEMATISCHE ZEITSCHRIFT | 2013年 / 275卷 / 1-2期

关键词：

Real algebraic variety; Pre-algebraic vector bundle; Algebraic vector bundle; Multiblowup; Regulous map; HOMOTOPY CLASSES;

D O I：

10.1007/s00209-012-1141-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let be a compact nonsingular affine real algebraic variety. We prove that every pre-algebraic vector bundle on becomes algebraic after finitely many blowing ups. Using this theorem, we then prove that the Stiefel-Whitney classes of any pre-algebraic -vector bundle on are algebraic. We also derive that the Chern classes of any pre-algebraic -vector bundles and the Pontryagin classes of any pre-algebraic -vector bundle are blow--algebraic. We also provide several results on line bundles on .

引用

页码：403 / 418

页数：16

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