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## Subvarieties of hypercomplex manifolds with holonomy in SL(n,H)

Cornell University
,
2012.
No. 1202.0222v1.

Soldatenkov A. O., Verbitsky M.

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 additional assumptions (Obata holonomy contained in SL(n,H), existence of an HKT metric), we prove that (M,L) contains no divisors, and all complex subvarieties of codimension 2 are trianalytic (that is, also hypercomplex).

Andrey Soldatenkov, International Mathematics Research Notices 2012 Vol. 2012 No. 15 P. 3483–3497

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 ...

Added: January 17, 2013

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

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

Kaledin D., Moscow Mathematical Journal 2012 Vol. 12 No. 3 P. 593–604

We give a direct interpretation of the Witt vector product in terms of tame residue in algebraic K-theory. ...

Added: October 25, 2012

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

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

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

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 E., Cerulli Irelli G., Reineke M., / Cornell University. Series math "arxiv.org". 2012. No. 1209.3960.

A desingularization of arbitrary quiver Grassmannians for representations of Dynkin quivers is constructed in terms of quiver Grassmannians for an algebra derived equivalent to the Auslander algebra of the quiver. ...

Added: October 9, 2012

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

Boston: International Pre, 2012.

Lively and engaging articles from the lecturers and the participants of the 18th Gökova Geometry-Topology Conference, held on the shores of Gökova Bay, Turkey, in May of 2011. ...

Added: September 6, 2012

Kiritchenko V., Smirnov E., Timorin V., Успехи математических наук 2012 Т. 67 № 4 С. 89–128

We describe a new approach to the Schubert calculus on complete flag varieties using the volume polynomial associated with Gelfand-Zetlin polytopes. This approach allows us to compute the intersection products of Schubert cycles by intersecting faces of a polytope. ...

Added: September 19, 2012

Verbitsky M., Geometry and Topology 2014 Vol. 18 No. 2 P. 897–909

A Hermitian metric ω on a complex manifold is called SKT or pluriclosed if ddcω=0. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case M is Kähler, hence isomorphic to CP3 or a flag space. This result is obtained from rational ...

Added: April 29, 2014

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

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

Verbitsky M., Pure and Applied Mathematics Quarterly 2014 Vol. 10 No. 2 P. 325–354

Let S be a smooth rational curve on a complex manifold M. It is called ample if its normal bundle is positive: NS=⨁O(i_k),i_k<0. We assume that M is covered by smooth holomorphic deformations of S. The basic example of such a manifold is a twistor space of a hyperkähler or a 4–dimensional anti-selfdual Riemannian manifold ...

Added: January 23, 2015

Cerulli Irelli G., Feigin E., Reineke M., / Cornell University. Series math "arxiv.org". 2012. No. 1206.4178.

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study ...

Added: June 29, 2012

Malyshev D., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2020 Vol. 14 No. 4 P. 706–721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

Malyshev D., Alekseev V., Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3–10

Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...

Added: August 31, 2012

Danilov V., Rakhel M., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 179–187

In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations. ...

Added: June 6, 2021

P.: Université Paris 13 - Paris Sorbonne Cité, 2013.

In this workshop we will bring together participants who have solutions for one or more of the following problems: How can mutual understanding be optimized with the help of technology in hospitals where both patients and professionals have varying language skills, cultural backgrounds and cognitive capacities? Can domain ontologies, natural language processing tools, multilingual knowledge-based ...

Added: December 18, 2014

Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283–291

The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...

Added: December 7, 2013

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268–1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014

Akopov A. S., Beklaryan L. A., Saghatelyan A. K., Environmental Modelling and Software 2019 Vol. 116 P. 7–25

Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...

Added: February 24, 2019