Geodesic
An algebraic C2–equivariant Bézout theorem
Costenoble, Steven R1 ; Hudson, Thomas2 ; Tilson, Sean3
1 Department of Mathematics, Hofstra University, Hempstead, NY, United States
2 College of Transdisciplinary Studies, DGIST, Daegu, South Korea
3 Hörstel, Germany
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2331-2350

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

One interpretation of Bézout’s theorem, nonequivariantly, is as a calculation of the Euler class of a sum of line bundles over complex projective space, expressing it in terms of the rank of the bundle and its degree. We generalize this calculation to the C2–equivariant context, using the calculation of the cohomology of C2–complex projective spaces from an earlier paper, which used ordinary C2–cohomology with Burnside ring coefficients and an extended grading necessary to define the Euler class. We express the Euler class in terms of the equivariant rank of the bundle and the degrees of the bundle and its fixed subbundles. We do similar calculations using constant ℤ coefficients and Borel cohomology and compare the results.

DOI : 10.2140/agt.2024.24.2331
Keywords: equivariant cohomology, equivariant characteristic classes, projective space, Bézout's theorem

Costenoble, Steven R 1 ; Hudson, Thomas 2 ; Tilson, Sean 3

1 Department of Mathematics, Hofstra University, Hempstead, NY, United States
2 College of Transdisciplinary Studies, DGIST, Daegu, South Korea
3 Hörstel, Germany 
@article{10_2140_agt_2024_24_2331,
     author = {Costenoble, Steven R and Hudson, Thomas and Tilson, Sean},
     title = {An algebraic {C2{\textendash}equivariant} {B\'ezout} theorem},
     journal = {Algebraic and Geometric Topology},
     pages = {2331--2350},
     publisher = {mathdoc},
     volume = {24},
     number = {4},
     year = {2024},
     doi = {10.2140/agt.2024.24.2331},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2331/}
}
TY  - JOUR
AU  - Costenoble, Steven R
AU  - Hudson, Thomas
AU  - Tilson, Sean
TI  - An algebraic C2–equivariant Bézout theorem
JO  - Algebraic and Geometric Topology
PY  - 2024
SP  - 2331
EP  - 2350
VL  - 24
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2331/
DO  - 10.2140/agt.2024.24.2331
ID  - 10_2140_agt_2024_24_2331
ER  - 
%0 Journal Article
%A Costenoble, Steven R
%A Hudson, Thomas
%A Tilson, Sean
%T An algebraic C2–equivariant Bézout theorem
%J Algebraic and Geometric Topology
%D 2024
%P 2331-2350
%V 24
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.2331/
%R 10.2140/agt.2024.24.2331
%F 10_2140_agt_2024_24_2331
Costenoble, Steven R; Hudson, Thomas; Tilson, Sean. An algebraic C2–equivariant Bézout theorem. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2331-2350. doi: 10.2140/agt.2024.24.2331

Cité par Sources :