Equivariant Algebraic Vector Bundles Over Representations — A Survey

2002 ◽  
pp. 25-36
Author(s):  
Mikiya Masuda
Keyword(s):  
Vector Bundles ◽  
Algebraic Vector

scholarly journals EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES, INTEGRALITY AND LINEAR SUBSPACES OF COMPLETE INTERSECTIONS

2021 ◽  
pp. 1-66
Author(s):  
Tom Bachmann ◽  
Kirsten Wickelgren
Keyword(s):  
Commutative Algebra ◽  
Vector Bundles ◽  
Euler Class ◽  
Complete Intersections ◽  
Bilinear Forms ◽  
Euler Numbers ◽  
Coherent Sheaves ◽  
Linear Subspaces ◽  
Algebraic Vector

Abstract We equate various Euler classes of algebraic vector bundles, including those of [12] and one suggested by M. J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class and give formulas for local indices at isolated zeros, both in terms of the six-functors formalism of coherent sheaves and as an explicit recipe in the commutative algebra of Scheja and Storch. As an application, we compute the Euler classes enriched in bilinear forms associated to arithmetic counts of d-planes on complete intersections in $\mathbb P^n$ in terms of topological Euler numbers over $\mathbb {R}$ and $\mathbb {C}$ .

scholarly journals Algebraic vector bundles over the $l$-hole torus

1975 ◽  
Vol 19 (3) ◽  
pp. 336-343 ◽  
Author(s):  
Joseph M. Cavanaugh
Keyword(s):  
Vector Bundles ◽  
Algebraic Vector

scholarly journals Algebraic Vector Bundles on $SL(3,{\bf C})$

2007 ◽  
Vol 37 (2) ◽  
pp. 587-596
Author(s):  
Kazunori Nakamoto ◽  
Takeshi Torii
Keyword(s):  
Vector Bundles ◽  
Algebraic Vector

CLASSIFICATION OF REAL ALGEBRAIC VECTOR BUNDLES OVER THE REAL ANISOTROPIC CONIC

2005 ◽  
Vol 16 (10) ◽  
pp. 1207-1220 ◽  
Author(s):  
INDRANIL BISWAS ◽  
D. S. NAGARAJ
Keyword(s):  
Vector Bundles ◽  
Complete Classification ◽  
Real Numbers ◽  
The Real ◽  
Isomorphism Classes ◽  
Algebraic Vector

We give a complete classification of isomorphism classes of real algebraic vector bundles over the scheme defined by a nondegenerate anisotropic conic defined over the field of real numbers.

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