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Holonomy of the Obata connection on SU(3)
International Mathematics Research Notices. 2012. Vol. 2012. No. 15. P. 3483-3497.
Andrey Soldatenkov
A hypercomplex structure on a smooth manifold is a triple of integrable almost complex structures satisfying quaternionic relations. The Obata connection is the unique torsion-free connection that preserves each of the complex structures. The holonomy group of the Obata connection is contained in GL(n, H). There is a well-known construction of hypercomplex structures on Lie groups due to Joyce. In this paper we show that the holonomy of the Obata connection on SU(3) coincides with GL(2, H).
Soldatenkov A. O., Verbitsky M., / Cornell University. Series math "arxiv.org". 2012. No. 1202.0222v1.
A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. For each quaternion L=aI +bJ+cK, L^2=-1, L is also a complex structure operator on M, called an induced complex structure. We are studying compact complex subvarieties of (M,L), when L is a generic induced complex structure. Under ...
Added: July 25, 2012
Soldatenkov A. O., Verbitsky M., International Mathematics Research Notices 2013
A hypercomplex manifold is a manifold equipped with a triple of complex structures satisfying the quaternionic relations. A holomorphic Lagrangian variety on a hypercomplex manifold with trivial canonical bundle is a holomorphic subvariety which is calibrated by a form associated with the holomorphic volume form; this notion is a generalization of the usual holomorphic Lagrangian ...
Added: October 8, 2013
Andrey Soldatenkov, Verbitsky M., / Cornell University. Series math "arxiv.org". 2013.
A hypercomplex manifold is a manifold equipped with a triple of complex structures satisfying the quaternionic relations. A holomorphic Lagrangian variety on a hypercomplex manifold with trivial canonical bundle is a holomorphic subvariety which is calibrated by a form associated with the holomorphic volume form; this notion is a generalization of the usual holomorphic Lagrangian ...
Added: December 22, 2013
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We construct a curve in the unstable foliation of an Anosov diffeomorphism such that the holonomy along this curve is defined on all of the corresponding stable leaves. ...
Added: September 30, 2013
Trubochkina N. K., Качество. Инновации. Образование 2012 Т. 84 № 5 С. 76-82
Scientific and exploratory research and mathematical simulation of a fractal designresults are presented. Decorative fractal patterns for textile and construction industries (models, murals, stained glass) have been developed. Fractals, which can be attributed to a class of fractal artdeveloped. Technology of frost-and water-resistant seamless large area fractal frescoes developed. Technology cost much less than for ...
Added: November 21, 2012
Providence : American Mathematical Society, 2012
The volume is to contain the proceedings of the 13th conference AGCT as well as the proceedings of the conference Geocrypt. The conferences focus on various aspects of arithmetic and algebraic geometry, number theory, coding theory and cryptography. The main topics discussed at conferences include the theory of curves over finite fields, theory of abelian ...
Added: January 3, 2013
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 2 P. 337-361
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand-Tsetlin subalgebra of U(gln), and formulate a conjectural answer for the small quantum cohomology rings in terms of ...
Added: October 9, 2012
Déev R. N., / Cornell University. Series arXiv "math". 2016.
Essential dimension of a family of complex manifolds is the dimension of the image of its base in the Kuranishi space of the fiber. We prove that any family of hyperk\"ahler manifolds over a compact simply connected base has essential dimension not greater than 1. A similar result about families of complex tori is also ...
Added: September 23, 2016
Prokhorov Y., Journal of Algebraic Geometry 2012 Vol. 21 No. 3 P. 563-600
We classify all finite simple subgroups of the Cremona group Cr3(C). ...
Added: September 19, 2012
Kurnosov N., / Cornell University. Series math "arxiv.org". 2014.
Let M be a compact irreducible hyperkahler manifold, from Bogomolov inequality [V1] we obtain forbidden values of the second Betti number b_2 in arbitrary dimension. ...
Added: February 21, 2014
Feigin E., Cerulli Irelli G., Reineke M., Algebra & Number Theory 2012 Vol. 6 No. 1 P. 165-194
Quiver Grassmannians are varieties parametrizing subrepresentations of a quiver representation. It is observed that certain quiver Grassmannians for type A quivers are isomorphic to the degenerate flag varieties investigated earlier by the second named author. This leads to the consideration of a class of Grassmannians of subrepresentations of the direct sum of a projective and ...
Added: June 29, 2012
Kurnosov N., / Cornell University. Series math "arxiv.org". 2015.
We prove that a generic complex deformation of a generalized Kummer variety contains no complex analytic tori. ...
Added: October 16, 2015
Feigin B. L., Buryak A., Journal of Geometry and Physics 2012 Vol. 62 No. 7 P. 1652-1664
The moduli space M(r,n) of framed torsion free sheaves on the projective plane with rank r and second Chern class equal to n has the natural action of the (r+2)-dimensional torus. In this paper, we look at the fixed point set of different one-dimensional subtori in this torus. We prove that in the homogeneous case ...
Added: September 20, 2012
Feigin M., Shramov K., International Mathematics Research Notices 2012 Vol. 2012 No. 15 P. 3375-3414
We consider representations of rational Cherednik algebras that are particular ideals in the ring of polynomials. We investigate convergence of the integrals that express the Gaussian inner product on these representations. We derive that the integrals converge for the minimal submodules in types B and D for the singular values suggested by Cherednik with at ...
Added: September 13, 2012
Oberwolfach : European Mathematical Society Publishing house, 2012
В сборнике печатаются труды конференций Математического Института Обервольфаха. ...
Added: November 17, 2012
Ivan Cheltsov, Martinez-Garcia J., / Cornell University. Series math "arxiv.org". 2014.
For every smooth del Pezzo surface $S$, smooth curve $C\in|-K_{S}|$ and $\beta\in(0,1]$, we compute the $\alpha$-invariant of Tian $\alpha(S,(1-\beta)C)$ and prove the existence of K\"ahler--Einstein metrics on $S$ with edge singularities along $C$ of angle $2\pi\beta$ for $\beta$ in certain interval. In particular we give lower bounds for the invariant $R(S,C)$, introduced by Donaldson as ...
Added: February 5, 2015
Soldatenkov A. O., Verbitsky M., Journal of Geometry and Physics 2012 Vol. 62 No. 11 P. 2234-2240
A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. For each quaternion L=aI+bJ+cK, L2=−1, L is also a complex structure operator on M, called an induced complex structure. We study compact complex subvarieties of (M,L), for L a generic induced complex structure. Under additional assumptions (Obata ...
Added: August 30, 2012
Verbitsky M., Grantcharov G., Lejmi M., / Cornell University. Series math "arxiv.org". 2014.
A hypercomplex manifold M is a manifold equipped with three complex structures satisfying quaternionic relations. Such a manifold admits a canonical torsion-free connection preserving the quaternion action, called Obata connection. A quaternionic Hermitian metric is a Riemannian metric on which is invariant with respect to unitary quaternions. Such a metric is called HKT if it ...
Added: September 19, 2014
Popov V., / Centro Internazionale per la Ricerca Matematica. Series CIRM "Electronic preprint server". 2012. No. нет.
Some problems on the structure of the Cremona groups formulated (with comments) by the author at the International conference Birational and Affine Geometry, Levico Terme (Trento), 29.10.12--03.11.12 ...
Added: January 9, 2013
Kamenova L., Lu S., Verbitsky M., / Cornell University. Series math "arxiv.org". 2013.
The Kobayashi pseudometric on a complex manifold $M$ is the maximal pseudometric such that any holomorphic map from the Poincare disk to $M$ is distance-decreasing. Kobayashi has conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, we prove this result for any hyperkaehler manifold if it admits a deformation with a ...
Added: August 28, 2013
Feigin E., Selecta Mathematica, New Series 2012 Vol. 18 No. 3 P. 513-537
Let Fλ be a generalized flag variety of a simple Lie group G embedded into the projectivization of an irreducible G-module Vλ. We define a flat degeneration Fλa, which is a GaM variety. Moreover, there exists a larger group Ga acting on Fλa, which is a degeneration of the group G. The group Ga contains ...
Added: August 31, 2012
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...
Added: October 9, 2012
Verbitsky M., / Cornell University. Series math "arxiv.org". 2013.
Let M be a hyperkaehler manifold, and η a closed, positive (1,1)-form which is degenerate everywhere on M. We associate to η a family of complex structures on M, called a degenerate twistor family, and parametrized by a complex line. When η is a pullback of a Kaehler form under a Lagrangian fibration L, all ...
Added: December 27, 2013
M. : Higher School of Economics Publishing House, 2012
Toric geometry exhibited a profound relation between algebra and topology on one side and combinatorics and convex geometry on the other side. In the last decades, the interplay between algebraic and convex geometry has been explored and used successfully in a much more general setting: first, for varieties with an algebraic group action (such as ...
Added: November 17, 2012