Coherent sheaves and algebraic vector bundles

1985 ◽  
Vol 31 (1) ◽  
pp. 99-123 ◽  
Author(s):  
Alberto Tognoli
Keyword(s):  
Vector Bundles ◽  
Coherent Sheaves ◽  
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 Vector bundles associated to Lie algebras

2016 ◽  
Vol 2016 (716) ◽  
Author(s):  
Jon F. Carlson ◽  
Eric M. Friedlander ◽  
Julia Pevtsova
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Vector Bundles ◽  
Coherent Sheaves ◽  
Restricted Lie Algebra ◽  
Finite Dimensional

AbstractWe introduce and investigate a functorial construction which associates coherent sheaves to finite dimensional (restricted) representations of a restricted Lie algebra

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 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 Spherical Hall Algebras of Weighted Projective Curves

2018 ◽  
Vol 2020 (15) ◽  
pp. 4721-4775
Author(s):  
Jyun-Ao Lin
Keyword(s):  
Vector Bundles ◽  
Characteristic Functions ◽  
Projective Curve ◽  
Hall Algebra ◽  
Smooth Projective Curve ◽  
Coherent Sheaves ◽  
Hall Algebras ◽  
Arbitrary Genus ◽  
Projective Curves ◽  
Fixed Rank

Abstract In this article, we deal with the structure of the spherical Hall algebra $\mathbf{U}$ of coherent sheaves with parabolic structures on a smooth projective curve $X$ of arbitrary genus $g$. We provide a shuffle-like presentation of the bundle part $\mathbf{U}^>$ and show the existence of generic spherical Hall algebra of genus $g$. We also prove that the algebra $\mathbf{U}$ contains the characteristic functions on all the Harder–Narasimhan strata. These results together imply Schiffmann’s theorem on the existence of Kac polynomials for parabolic vector bundles of fixed rank and multi-degree over $X$. On the other hand, the shuffle structure we obtain is new and we make links to the representations of quantum affine algebras of type $A$.

scholarly journals Algebraic vector bundles on projective spaces: A problem list

Topology ◽  
1979 ◽  
Vol 18 (2) ◽  
pp. 117-128 ◽  
Author(s):  
Robin Hartshorne
Keyword(s):  
Vector Bundles ◽  
Projective Spaces ◽  
Problem List ◽  
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
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