Homogeneous instanton bundles on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">P</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math> for the action of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inline" overflow="scroll"><mml:mstyle mathvariant="sans-serif"><mml:mi>SL</mml:mi></mml:mstyle><mml:mrow><mml:mo>(</mml:mo><mml:m

Faenzi, Daniele

doi:10.1016/j.geomphys.2007.06.003

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…Remark 2.1. For d = 3 our result agrees with the resolution-theoretic approach to the construction of SL 2 (C)-equivariant instantons achieved in [Fae07]. In fact, in that paper the classification of instantons on P 3 which are invariant for any linear action of SL 2 (C) on P 3 was completed.…”

Section: The Pulled-back Kernel Bundlesupporting

confidence: 85%

“…Finally, for n = 1 and d = 3, our bundles agree with the SL 2 (C)-invariant instantons defined and studied in [Fae07]. These instantons are parametrized by N in the sense that the second Chern class (the so-called the "charge") of an SL 2 (C)-invariant instanton over P 3 = P(V 3 ) must equal m 2 for some integer m 2, and given such m there is one and only one such instanton.…”

Section: Introductionsupporting

confidence: 70%

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A construction of equivariant bundles on the space of symmetric forms

Boralevi¹,

Faenzi²,

Lella³

2018

Preprint

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We construct stable vector bundles on the space P(S d C n+1 ) of symmetric forms of degree d in n + 1 variables which are equivariant for the action of SLn+1(C), and admit an equivariant free resolution of length 2. For n = 1, we obtain new examples of stable vector bundles of rank d − 1 on P d , which are moreover equivariant for SL2(C). The presentation matrix of these bundles attains Westwick's upper bound for the dimension of vector spaces of matrices of constant rank and fixed size.

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Section: The Pulled-back Kernel Bundlesupporting

confidence: 85%

Section: Introductionsupporting

confidence: 70%

A construction of equivariant bundles on the space of symmetric forms

Boralevi¹,

Faenzi²,

Lella³

2018

Preprint

Self Cite

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Even and odd instanton bundles on Fano threefolds of Picard number one

Faenzi

2013

manuscripta math.

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We consider an analogue of the notion of instanton bundle on the projective 3-space, consisting of a class of rank-2 vector bundles defined on smooth Fano threefolds X of Picard number one, having even or odd determinant according to the parity of K X .We first construct a well-behaved irreducible component of their moduli spaces. Then, when the intermediate Jacobian of X is trivial, we look at the associated monads, hyperdeterminants and nets of quadrics. We also study one case where the intermediate Jacobian of X is non-trivial, namely when X is the intersection of two quadrics in 5 , relating instanton bundles on X to vector bundles of higher rank on a the curve of genus 2 naturally associated 2000 Mathematics Subject Classification. Primary 14J60, 14F05. Key words and phrases. Instanton bundles, monads, Fano threefolds, semiorthogonal decomposition, nets of quadrics.The author was partially supported by ANR-09-JCJC-0097-0 INTERLOW and ANR GEOLMI.1 * 3 (−r X ) ≃ 1 , * 2 (−r X ) ≃ 2 . Set U = Hom X ( 2 , 3 ), and note that U ≃ Hom X ( 1 , 2 ).

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Homogeneous instanton bundles on P3 for the action of SL(

Cited by 2 publications

References 14 publications

A construction of equivariant bundles on the space of symmetric forms

A construction of equivariant bundles on the space of symmetric forms

Even and odd instanton bundles on Fano threefolds of Picard number one

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