Nondegenerate multidimensional matrices and instanton bundles

DOI10.1090/S0002-9947-02-03126-4zbMath1031.14004arXivmath/0103078MaRDI QIDQ3151273

Laura Costa, Giorgio Ottaviani

Publication date: 7 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0103078

zbMATH Keywords

geometric invariant theorymonadinstanton bundleGIT-quotients of affine varieties

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Homogeneous spaces and generalizations (14M17) Geometric invariant theory (14L24) Vector and tensor algebra, theory of invariants (15A72) Classification of affine varieties (14R05) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21)

Related Items

Moduli of autodual instanton bundles ⋮ Moduli spaces of rank 2 instanton sheaves on the projective space ⋮ Two infinite series of moduli spaces of rank 2 sheaves on \({\mathbb {P}}^3\) ⋮ \(H\)-instanton bundles on three-dimensional polarized projective varieties ⋮ Deformation theory of orthogonal and symplectic sheaves ⋮ Complex ADHM equations and sheaves on \(\mathbb P ^3\) ⋮ Even and odd instanton bundles on Fano threefolds of Picard number one ⋮ Homogeneous instanton bundles on \(\mathbb P^3\) for the action of \(\mathrm{SL}(2)\) ⋮ Instanton sheaves and representations of quivers ⋮ Irreducibility of the moduli space of orthogonal instanton bundles on \(\mathbb{P}^n\) ⋮ Yang–Mills instanton sheaves with higher topological charges ⋮ ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES ⋮ The Binet--Cauchy theorem for the hyperdeterminant of boundary format multi-dimensional matrices ⋮ Branes in the moduli space of framed sheaves

Uses Software

• Macaulay2

Cites Work

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• A criterion for detecting m-regularity
• Construction of instantons
• Monads and moduli of vector bundles
• Regularity of the moduli space of instanton bundles \(MI_{\mathbb{P}^3}\)(5)
• Singularities of hyperdeterminants
• Unstable hyperplanes for Steiner bundles and mulitdimensional matrices
• Mathematical instanton bundles on P2n+1
• Stability of Special Instanton Bundles on ℙ 2n + 1