scholarly journals Absolutely split real algebraic vector bundles over a real form of projective space

2007 ◽  
Vol 131 (7) ◽  
pp. 686-696 ◽  
Author(s):  
Indranil Biswas ◽  
D.S. Nagaraj
Keyword(s):  
Projective Space ◽  
Vector Bundles ◽  
Real Form ◽  
Algebraic Vector

scholarly journals The moduli of a class of rank 2 vector bundles on P3

1981 ◽  
Vol 84 ◽  
pp. 9-30 ◽  
Author(s):  
G. Pete Wever
Keyword(s):  
Projective Space ◽  
Vector Bundles ◽  
Finite Union ◽  
Stable Rank ◽  
Projective Varieties ◽  
Algebraic Vector ◽  
Rank 2 ◽  
Rank 2 Vector Bundles ◽  
Rank 2 Bundles

Barth and others [1], [2], [5] have begun the study of stable algebraic vector bundles of rank 2 on projective space. Maruyama [7] has shown that stable rank 2 bundles have a variety of moduli which is the finite union of quasi-projective varieties.

Algebraic vector bundles on projective space

1970 ◽  
Vol 10 (4) ◽  
pp. 298-304 ◽  
Author(s):  
A. V. Geramita ◽  
L. G. Roberts
Keyword(s):  
Projective Space ◽  
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 ON THE STABILITY OF SYZYGY BUNDLES

2011 ◽  
Vol 22 (04) ◽  
pp. 515-534 ◽  
Author(s):  
IUSTIN COANDĂ
Keyword(s):  
Projective Space ◽  
Complete Intersection ◽  
Vector Bundles ◽  
Elementary Proof ◽  
Base Point ◽  
Vector Spaces ◽  
Similar Argument ◽  
Vanishing Theorem ◽  
The Stability ◽  
Koszul Cohomology

We are concerned with the problem of the stability of the syzygy bundles associated to base-point-free vector spaces of forms of the same degree d on the projective space of dimension n. We deduce directly, from M. Green's vanishing theorem for Koszul cohomology, that any such bundle is stable if its rank is sufficiently high. With a similar argument, we prove the semistability of a certain syzygy bundle on a general complete intersection of hypersurfaces of degree d in the projective space. This answers a question of H. Flenner [Comment. Math. Helv.59 (1984) 635–650]. We then give an elementary proof of H. Brenner's criterion of stability for monomial syzygy bundles, avoiding the use of Klyachko's results on toric vector bundles. We finally prove the existence of stable syzygy bundles defined by monomials of the same degree d, of any possible rank, for n at least 3. This extends the similar result proved, for n = 2, by L. Costa, P. Macias Marques and R. M. Miro-Roig [J. Pure Appl. Algebra214 (2010) 1241–1262]. The extension to the case n at least 3 has been also, independently, obtained by P. Macias Marques in his thesis [arXiv:0909.4646/math.AG (2009)].

Hermitian–Einstein metrics and jumping lines forSp(n+1)-homogeneous bundles over ℙ2n+1

1993 ◽  
Vol 114 (3) ◽  
pp. 443-451
Author(s):  
Al Vitter
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Vector Bundles ◽  
Einstein Metrics ◽  
Einstein Metric ◽  
Holomorphic Vector Bundles ◽  
Kähler Form ◽  
Points Of View ◽  
The Stability ◽  
Complex Projective

Stable holomorphic vector bundles over complex projective space ℙnhave been studied from both the differential-geometric and the algebraic-geometric points of view.On the differential-geometric side, the stability ofE-→ ℙncan be characterized by the existence of a unique hermitian–Einstein metric onE, i.e. a metric whose curvature matrix has trace-free part orthogonal to the Fubini–Study Kähler form of ℙn(see [6], [7], and [13]). Very little is known about this metric in general and the only explicit examples are the metrics on the tangent bundle of ℙnand the nullcorrelation bundle (see [9] and [10]).

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 Quantum reconstruction for Fano bundles on projective space

2015 ◽  
Vol 218 ◽  
pp. 1-28
Author(s):  
Andrew Strangeway
Keyword(s):  
Projective Space ◽  
Vector Bundles ◽  
Quantum Cohomology ◽  
Lefschetz Theorem ◽  
Small Quantum ◽  
Low Degree ◽  
Reconstruction Theorem ◽  
Rank 2

AbstractWe present a reconstruction theorem for Fano vector bundles on projective space which recovers the small quantum cohomology for the projectivization of the bundle from a small number of low-degree Gromov-Witten invariants. We provide an extended example in which we calculate the quantum cohomology of a certain Fano 9-fold and deduce from this, using the quantum Lefschetz theorem, the quantum period sequence for a Fano 3-fold of Picard rank 2 and degree 24. This example is new, and is important for the Fanosearch program.

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