Special instanton bundles and poncelet curves

1987 ◽  
pp. 325-336 ◽  
Author(s):  
W. Böhmer ◽  
G. Trautmann
Keyword(s):  
Instanton Bundles

scholarly journals Instanton bundles on two Fano threefolds of index 1

2020 ◽  
Vol 32 (5) ◽  
pp. 1315-1336
Author(s):  
Gianfranco Casnati ◽  
Ozhan Genc
Keyword(s):  
Irreducible Component ◽  
Moduli Space ◽  
Blow Up ◽  
Explicit Construction ◽  
Fano Threefolds ◽  
Instanton Bundles

AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

scholarly journals Infinitesimal moduli of G2 holonomy manifolds with instanton bundles

2016 ◽  
Vol 2016 (11) ◽  
Author(s):  
Xenia de la Ossa ◽  
Magdalena Larfors ◽  
Eirik E. Svanes
Keyword(s):  
Instanton Bundles

scholarly journals Moduli of autodual instanton bundles

2016 ◽  
Vol 47 (3) ◽  
pp. 823-843 ◽  
Author(s):  
Marcos Jardim ◽  
Simone Marchesi ◽  
Anna Wissdorf
Keyword(s):  
Instanton Bundles

Regularity of the moduli space of instanton bundles MIP3(5)

2003 ◽  
Vol 8 (2) ◽  
pp. 147-158 ◽  
Author(s):  
Pavel I. Katsylo ◽  
Giorgio Ottaviani
Keyword(s):  
Moduli Space ◽  
Instanton Bundles

scholarly journals Instanton bundles on Fano threefolds

2012 ◽  
Vol 10 (4) ◽  
pp. 1198-1231 ◽  
Author(s):  
Alexander Kuznetsov
Keyword(s):  
Fano Threefolds ◽  
Instanton Bundles

scholarly journals Trihyperkähler reduction and instanton bundles on

2014 ◽  
Vol 150 (11) ◽  
pp. 1836-1868 ◽  
Author(s):  
Marcos Jardim ◽  
Misha Verbitsky
Keyword(s):  
Moduli Space ◽  
Twistor Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Rational Curves ◽  
Chern Connection ◽  
Symplectic Forms ◽  
Complex Dimension ◽  
Instanton Bundles ◽  
Hyperkähler Manifold

AbstractA trisymplectic structure on a complex $2n$-manifold is a three-dimensional space ${\rm\Omega}$ of closed holomorphic forms such that any element of ${\rm\Omega}$ has constant rank $2n$, $n$ or zero, and degenerate forms in ${\rm\Omega}$ belong to a non-degenerate quadric hypersurface. We show that a trisymplectic manifold is equipped with a holomorphic 3-web and the Chern connection of this 3-web is holomorphic, torsion-free, and preserves the three symplectic forms. We construct a trisymplectic structure on the moduli of regular rational curves in the twistor space of a hyperkähler manifold, and define a trisymplectic reduction of a trisymplectic manifold, which is a complexified form of a hyperkähler reduction. We prove that the trisymplectic reduction in the space of regular rational curves on the twistor space of a hyperkähler manifold $M$ is compatible with the hyperkähler reduction on $M$. As an application of these geometric ideas, we consider the ADHM construction of instantons and show that the moduli space of rank $r$, charge $c$ framed instanton bundles on $\mathbb{C}\mathbb{P}^{3}$ is a smooth trisymplectic manifold of complex dimension $4rc$. In particular, it follows that the moduli space of rank two, charge $c$ instanton bundles on $\mathbb{C}\mathbb{P}^{3}$ is a smooth complex manifold dimension $8c-3$, thus settling part of a 30-year-old conjecture.

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