Skip to main content Accessibility help
×
Home

On the quadratic invariant of binary sextics

  • MACIEJ DUNAJSKI (a1) and ROGER PENROSE (a2)

Abstract

We provide a geometric characterisation of binary sextics with vanishing quadratic invariant.

Copyright

References

Hide All
[1] Bryant, R. L. Metrics with exceptional holonomy. Ann. of Math. 126 (1987), 525576.
[2] Dolgachev, I. Lectures on Invariant Theory (Cambridge University Press, 2003).
[3] Doubrov, B. and Dunajski, M. Co–calibrated G 2 structure from cuspidal cubics. Ann. Global Anal. Geom. 42 (2012), 247265.
[4] Dunajski, M. and Godliński, M. GL(2, ℝ) structures, G 2 geometry and twistor theory. Quart. J. Math 63 (2012), 101132.
[5] Dunajski, M. and Sokolov, V. V. On 7th order ODE with submaximal symmetry. J. Geom. Phys. 61 (2011), 12581262.
[6] Eastwood, M. G. and Isaev, A. V. Extracting invariants of isolated hypersurface singularities from their moduli algebras. Math. Ann. 356 (2013), 7398.
[7] Elliott, E. B. An Introduction to the Algebra of Quantics (Oxford University Press, Clarendon Press, Oxford, 1895).
[8] Grace, J. H. and Young, A. The Algebra of Invariants (Cambridge University Press, Cambridge, 1903).
[9] Hitchin, N. Vector Bundles and the Icosahedron. Contemp. Math. 522 Amer. Math. Soc. (Providence, RI 2010), 7187.
[10] Igusa, J. I. Arithmetic variety of moduli of genus two. Ann. of Math. 72 (1960), 612649.
[11] Kodaira, K. On stability of compact submanifolds of complex manifolds. Amer. J. Math. 85 (1963), 7994.
[12] Kung, J. P. S. and Rota, G. The invariant theory of binary forms. Bull. AMS 10 (1984), 2785.
[13] Mumford, D., Fogarty, J. and Kirwan, F. Geometric Invariant Theory (Springer-Verlag, 1994).
[14] Olver, P. Classical Invariant Theory (Cambridge University Press, Cambridge, 1999).
[15] Penrose, R. Nonlinear gravitons and curved twistor theory. Gen. Rel. Grav. 7 (1976), 3152.
[16] Penrose, R. Orthogonality of general spin states. Twistor Newsletter 36 (1993).
[17] Penrose, R. and Rindler, W. Spinors and space-time. Two-spinor calculus and relativistic fields. Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 1987, 1988).
[18] Sylvester, J. J. On the calculus of forms, otherwise the theory of invariants. Cambridge and Dublin Mathematical Journal IX (1854), 85103.
[19] Sylvester, J. J. On an application of the new atomic theory to the graphical representation of the invariants and covariants of binary quantics, with three appendices. Amer. Journ. Math. I. (1878), 64125.
[20] Zimba, J. and Penrose, R. On Bell nonlocality without probabilities: more curious geometry. Stud. Hist. Philos. Sci. 24 (1993), 697720.

Related content

Powered by UNSILO

On the quadratic invariant of binary sextics

  • MACIEJ DUNAJSKI (a1) and ROGER PENROSE (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.