Vector Bundles on Complex Projective Spaces

Okonek, Christian; Schneider, Michael; Spindler, Heinz

doi:10.1007/978-1-4757-1460-9

Cited by 455 publications

(319 citation statements)

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“…For reviews of this construction and some of its applications, see Ref. [27,28,34]. The monad bundles V considered in this paper are defined through the short exact sequence…”

Section: The Monad Construction On Cicysmentioning

confidence: 99%

Monad bundles in heterotic string compactifications

Anderson

Lukas

2008

J. High Energy Phys.

106

204

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In this paper, we study positive monad vector bundles on complete intersection Calabi-Yau manifolds in the context of E 8 × E 8 heterotic string compactifications. We show that the class of such bundles, subject to the heterotic anomaly condition, is finite and consists of about 7000 models. We explain how to compute the complete particle spectrum for these models. In particular, we prove the absence of vector-like family anti-family pairs in all cases. We also verify a set of highly non-trivial necessary conditions for the stability of the bundles. A full stability proof will appear in a companion paper. A scan over all models shows that even a few rudimentary physical constraints reduces the number of viable models drastically.anderson@maths.ox.ac.uk

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“…For reviews of this construction and some of its applications, see Ref. [27,28,34]. The monad bundles V considered in this paper are defined through the short exact sequence…”

Section: The Monad Construction On Cicysmentioning

confidence: 99%

Monad bundles in heterotic string compactifications

Anderson

Lukas

2008

J. High Energy Phys.

106

204

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“…We want to investigate D when the arrangement is nongeneric; the tool will be the short exact sequence of the last section. We first recall a few standard results about vector bundles on P n , referring for proofs to the book of Okonek, Schneider and Spindler [13]. Definition 4.1.…”

Section: Stability and Jump Locimentioning

confidence: 99%

“…An easy application of the Beilinson spectral sequence [13] shows that a stable bundle with c 1 = −1 and c 2 = 1 must be Ω 1 P 2 (1), so for arrangement II, the jump locus of D is empty. For arrangement III, Barth's theorem implies that the support of j D is of degree one; by Theorem 4.7 {x + y = 0} and {y + z = 0} are jumping lines, hence j D is the line {x−y +z = 0} ⊆ P 2 ∨ .…”

Section: Theorem 47 Let a Be An Arrangement Of D Lines L ∈ A Andmentioning

confidence: 99%

Elementary modifications and line configurations in P^2

Schenck¹

2003

Comment. Math. Helv.

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Abstract. Associated to a projective arrangement of hyperplanes A ⊆ P n is the module D(A), which consists of derivations tangent to A. We study D(A) when A is a configuration of lines in P 2 . In this setting, we relate the deletion/restriction construction used in the study of hyperplane arrangements to elementary modifications of bundles. This allows us to obtain bounds on the Castelnuovo-Mumford regularity of D(A). We also give simple combinatorial conditions for the associated bundle to be stable, and describe its jump lines. These regularity bounds and stability considerations impose constraints on Terao's conjecture.

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“…Furthermore, there are no known examples on P n for n ≥ 5 and the Hartshorne conjecture predicts that none exist (at least for n ≥ 7;see [16]). …”

Section: Generic Splitting On Conicsmentioning

confidence: 99%

Restricting semistable bundles on the projective plane to conics

Vitter

2004

manuscripta math.

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Abstract. We study the restrictions of rank 2 semistable vector bundles E on P 2 to conics. A Grauert-Mülich type theorem on the generic splitting is proven. The jumping conics are shown to have the scheme structure of a hypersurface J 2 ⊂ P 5 of degree c 2 (E) when c 1 (E) = 0 and of degree c 2 (E) − 1 when c 1 (E) = −1. Some examples of jumping conics and jumping lines are studied in detail.

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Vector Bundles on Complex Projective Spaces

Cited by 455 publications

References 0 publications

Monad bundles in heterotic string compactifications

Monad bundles in heterotic string compactifications

Elementary modifications and line configurations in P^2

Restricting semistable bundles on the projective plane to conics

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