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Papers

• Geometry and automorphisms of non-Kähler holomorphic symplectic manifolds

  
  with E. Yasinsky , F. Bogomolov , A. Kuznetsova
  Published, IMRN (2022)
  [ arXiv pdf ] Abstract ± We consider the only one known class of non-Kähler irreducible holomorphic symplectic manifolds, described in the works of D. Guan and the first author. Any such manifold Q of dimension 2n-2 is obtained as a finite degree n^2 cover of some non-Kähler manifold W_F which we call the base of Q. We show that the algebraic reduction of Q and its base is the projective space of dimension n-1. Besides, we give a partial classification of submanifolds in Q and derive some consequences about its group of bimeromorphic automorphisms.

• Deformations of Lagrangian fibrations of holomorphically symplectic manifolds

  
  with M.Verbitsky
  In preparation
  Abstract ±

• Deformations and BBF-form of non-Kahler irreducible holomorphically symplectic manifolds

  
  with M. Verbitsky
  Submitted (2019)
  [ arXiv pdf ] Abstract ± In 1995, Dan Guan constructed examples of non-Kahler, simply-connected holomorphically symplectic manifolds. An alternative construction, using the Hilbert scheme of Kodaira-Thurston surface, was given by F. Bogomolov. We investigate topology and deformation theory of Bogomolov-Guan manifolds and show that it is similar to that of hyperkahler manifolds. We prove the local Torelli theorem, showing that holomorphically symplectic deformations of BG-manifolds are unobstructed, and the corresponding period map is locally a diffeomorphism. Using the local Torelli theorem, we prove the Fujiki formula for a BG-manifold M. This form is a non-Kahler version of the Beauville-Bogomolov-Fujiki form known in hyperkahler geometry.

• Kuga-Satake construction and cohomology of hyperkahler manifolds

  
  with A. Soldatenkov and M. Verbitsky
  Advances in Mathematics 351, 275-295 (2019)
  [ arXiv pdf ] Abstract ± Let M be a simple hyperkahler manifold. Kuga-Satake construction gives an embedding of H 2 (M, C) into the second cohomology of a torus, compatible with the Hodge structure. We construct a torus T and an embedding of the graded cohomology space H*(M, C)->H*+l (T, C) for some l, which is compatible with the Hodge structures and the Poincare pairing. Moreover, this embedding is compatible with an action of the Lie algebra generated by all Lefschetz sl (2)-triples on M.

• Automorphisms of hyperkahler manifolds and groups acting on CAT(0) spaces

  
  with E. Yasinsky
  Published in Springer Proceedings: Birational geometry, Kahler–Einstein metrics and degenerations (2022)
  [ arXiv pdf ] Abstract ± We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperkahler manifolds. Using an action of these groups on some non-positively curved space, we deduce many of their properties, including finite presentation, strong form of Tits' alternative and some structural results about groups consisting of transformations with infinite order.

• Lagrangian fibrations of IHS fourfolds

  
  with F. Bogomolov
  Submitted, EJM (2019)
  [ arXiv pdf ] Abstract ± In this paper we study the Lagrangian fibrations for projective irreducible symplectic fourfolds and exclude the case of non-smooth base. Our method could be extended to the higher-dimensional cases.

• Classifying VII0 surfaces with b2=0 via group theory

  
  with F. Bogomolov and F. Buonerba
  to appear, EJM
  [ arXiv pdf ] Abstract ± ...

• Absolutely trianalytic tori in the generalized Kummer variety

  
  Advances in Mathematics 298, 473-483 (2016)
  [ arXiv pdf ] Abstract ± ...

• Inequalities for Betti numbers of hyperkahler manifolds in dimension six

  
  Mathematical Notes 99 (1-2), 330-334 (2016)
  [ pdf ] Abstract ± ...

• Boundness of b_2 for hyperkahler manifolds with vanishing odd-Betti numbers

  
  Mathematical Notes (to appear, 2020)
  [ pdf , Arxiv, 1511.02838 ] Abstract ± ...

• Constraints for Betti numbers of hyperkahler manifolds in dimension six

  
  to appear in Proceedings of miniPAGES
  Abstract ± ...

• The second Betti number of hyperkahler manifolds

  
  Arxiv, 1401.0510 [math.AG].

• Absolutely trianalytic tori in the generalized Kummer variety

  
  (in Russian) Koryazhma, August, , pp. 50-51, 2015.

• On the boundness of Betti numbers of hyperkahler manifolds

  
  (in Russian) Koryazhma, August, pp. 31-33, 2016
  

  Chemistry

• (2-Benzoyl-1-phenylethenolato-k2O, O') bis [2-(1-phenyl-1H-benzimidazol-2-yl) phenyl-kC1] iridium (III) dichloromethane disolvate

  with SI Bezzubov, VD Doljenko, NM Kurnosov, IS Zharinova, IV Kovalenko
  IUCrData 1 (12), x161915
  Abstract ± n/a

• Synthesis and Structure of New Copper(II) Nitrate Complexes with 2,6-Bis(pyrazolyl)pyridine

  with V. Dolzhenko, S. Troyanov
  Z. Anorg. Allg. Chem. 2014 , 640, (2), 347-351
  Abstract ± Three mononuclear copper(II) complexes of copper nitrate with 2,6-bis(pyrazol-1-yl)pyridine (bPzPy) and 2, 6-bis(3',5'-dimethylpyrazol-1-yl)pyridine (bdmPzPy), [Cu(bPzPy)(NO3)2] (1), [Cu(bPzPy)(H2O)(NO3)2] (2) and [Cu(bdmPzPy)(NO3)2] (3) were synthesized by the reaction of copper nitrate with the ligand in ethanol solution. The complexes have been characterized through analytical, spectroscopic and EPR measurements. Single crystal X-ray structure analysis of complexes 1 and 2 revealed a five-coordinate copper atom in 1, whereas 2 contains a six-coordinate (4+2) CuII ion with molecular units acting as supramolecular nodes. These neutral nodes are connected through O-H---O(nitrate) hydrogen bonds to give couples of parallel linear strips assembled in 1D-chains in a zipper-like motif.

• Synthesis of thienylpyrazoles

  
  HGS, 16, pp. 14-21, 2015
  Abstract ± ...

• Local sections and the base of Lagrangian fibrations of IHS (joint with F. Bogomolov), in preparation.
• Automorphisms and subvarieties of non-Kahler IHS (joint with E. Yasinsky, F. Bogomolov, and A. Kuznetsova), in progress.
• Rozansky-Witten invariants: from Kahler case to non-Kahler.
• Hyperkahlers over finite fields, lifting and Kuga-Satake.
• Hodge ring of hk manifolds.

• LXXV Moscow Matematical Olympiad

  (as one of authors), M.: MCCME, 2012, 72 pages.

• LXXVI Moscow Matematical Olympiad

  (as one of authors), M.: MCCME, 2013, 78 pages.

• LXXIX Moscow Matematical Olympiad

  (as one of authors), M.: MCCME, 2016, 65 pages.

• Problems of Moscow Chemical Tournaments

  (as one of authors), M.: MCCME, 2015, 44 pages.

• Problems of Moscow Chemical Tournaments

  (as one of authors), M.: MCCME, 2016, 48 pages. (second edition)