Holomorphic and algebraic vector bundles on 0-convex algebraic surfaces

1999 ◽  
Vol 109 (4) ◽  
pp. 353-358
Author(s):  
E. Ballico ◽  
E. Gasparim
Keyword(s):  
Vector Bundles ◽  
Algebraic Surfaces ◽  
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 Complete algebraic vector fields on affine surfaces

2020 ◽  
Vol 31 (03) ◽  
pp. 2050018
Author(s):  
Shulim Kaliman ◽  
Frank Kutzschebauch ◽  
Matthias Leuenberger
Keyword(s):  
Algebraic Surface ◽  
Vector Fields ◽  
Algebraic Surfaces ◽  
Algebraic Vector ◽  
Dual Graphs ◽  
Holomorphic Automorphisms

Let [Formula: see text] be the subgroup of the group [Formula: see text] of holomorphic automorphisms of a normal affine algebraic surface [Formula: see text] generated by elements of flows associated with complete algebraic vector fields. Our main result is a classification of all normal affine algebraic surfaces [Formula: see text] quasi-homogeneous under [Formula: see text] in terms of the dual graphs of the boundaries [Formula: see text] of their SNC-completions [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document