Vector Bundles on Complex Projective Spaces

Okonek, Christian; Schneider, C.; Spindler, Heinz

doi:10.1007/978-3-0348-0151-5

Cited by 534 publications

(617 citation statements)

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“…When E = T X, the sheaf F 1 is known as the obstruction bundle 13 , as we shall now check. First, a couple of easy tests of this statement.…”

Section: More General Bundles Presented As Cokernelsmentioning

confidence: 96%

“…Far worse now is the case of a family of curves, in which the cohomology of the restriction of E can jump in the family [13]. If the cohomology of the restriction of E jumps, then surely the corresponding numerical factor jumps, and so the required integral over the moduli space of zero modes can not have nearly so simple a form as appeared in [14].…”

Section: Generalitiesmentioning

confidence: 99%

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Notes on Certain (0,2) Correlation Functions

Katz

Sharpe

2005

Commun. Math. Phys.

249

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In this paper we shall describe some correlation function computations in perturbative heterotic strings that, for example, in certain circumstances can lend themselves to a heterotic generalization of quantum cohomology calculations. Ordinary quantum chiral rings reflect worldsheet instanton corrections to correlation functions involving products of elements of Dolbeault cohomology groups on the target space. The heterotic generalization described here involves computing worldsheet instanton corrections to correlation functions defined by products of elements of sheaf cohomology groups. One must not only compactify moduli spaces of rational curves, but also extend a sheaf (determined by the gauge bundle) over the compactification, and linear sigma models provide natural mechanisms for doing both. Euler classes of obstruction bundles generalize to this language in an interesting way.

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“…When E = T X, the sheaf F 1 is known as the obstruction bundle 13 , as we shall now check. First, a couple of easy tests of this statement.…”

Section: More General Bundles Presented As Cokernelsmentioning

confidence: 96%

Section: Generalitiesmentioning

confidence: 99%

Notes on Certain (0,2) Correlation Functions

Katz

Sharpe

2005

Commun. Math. Phys.

249

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“…. , z 4 , this vector bundle is well-defined over the projective space CP 3 [22]. With respect to ordered bases (u 1 , .…”

Section: 1mentioning

confidence: 99%

The Adhm Construction of Instantons on Noncommutative Spaces

Brain

Suijlekom

2011

Rev. Math. Phys.

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Abstract. We present an account of the ADHM construction of instantons on Euclidean space-time R 4 from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parameterised by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal-Groenewold plane R 4 and the Connes-Landi plane R 4 θ .

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“…between homomorphisms of bundles and homomorphisms of monads (see for example Lemma II.4.1.3 in [14]). Hence, an isomorphism ϕ : E → E ∨ can be lifted to an isomorphism of monads…”

Section: Proof Considering the Monad Which Defines E (2)mentioning

confidence: 99%