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Библиография (TeX)
Аннотированная библиография статей
моих по математике за последние 2 года, по-английски.
Написано для каких-то технических надобностей.

Вот


A few papers dedicated to hypercomplex manifolds
equipped with HKT-metrics. New examples, based on cotangent
and tangent bundes to HKT-manifolds, were obtained
\cite{_Verbitsky_HKT-exa_}. Vanishing theorems, based
on supersymmetry, obtained (\cite{_Verbitsky:HKT_}
\cite{_Verbitsky:LCHK_}). The last of these papers
deals with locally conformal hyperkaehler geometry,
giving a structure theorem for compact locally conformal
hyperkaehler manifolds. Similar structure theorem was
obtained jointly with L. Ornea (\cite{_OV:Structure_})
for Vaisman (generalized Hopf) manifolds. By means of structure
theorem, we reduced all Vaisman geometry to 1-Sasakian
geometry. This was a basis for our next work
(\cite{_OV:Immer_}), where a Kodaira-type embedding
theorem was proven for compact Vaisman manifolds. We found
that any Vaisman manifold can be holomorphically
embedded to an appropriate Hopf manifold, and conversely,
any submanifold of a Hopf manifold is Vaisman.
This has profound implications for 1-Sasakian geometry:
any compact 1-Sasakian manifold can be deformed to one where
the Reeb field has compact orbits.

Two papers on the category of coherent
sheaves on generic K3 surfaces and tori. It was shown
(\cite{_Verbitsky:cohe_}, \cite{_Verbitsky:tori_})
that this category is isomorphic for all generic tori
of the same dimension and for all generic K3-surfaces.
This was done using Yang-Mills theory and twistor geometry
of hyperkaehler metric. For odd-dimensional tori, which
don't admit hyperkaehler metrics, I used the
``$SO(2n)/U(n)$-twistor space'' invented for
this purpose. It is a holomorphic deformation
of a torus, with a base isomorphic to a
Hermitian symmetric manifold $SO(2n)/U(n)$.
In most respects (twistor sections, twistor transform)
the $SO(2n)/U(n)$-twistor space
is similar to the usual hyperkaehler
twistor space.

{\scriptsize
\begin{thebibliography}{XXX}

\bibitem[OV1]{_OV:Structure_}
L. Ornea, M. Verbitsky, {\em Structure theorem for compact Vaisman
ma\-ni\-folds}, http://arxiv.org/abs/math.DG/0305259, 8 pages.

\bibitem[OV2]{_OV:Immer_}
L. Ornea, M. Verbitsky, {\em
Immersion theorem for Vaisman manifolds},
http://arxiv.org/abs/math.AG/0306077, 28 pages


\bibitem[V1]{_Verbitsky:HKT_}
Verbitsky, M.,
{\em Hyperk\"ahler manifolds with torsion, supersymmetry and Hodge theory},
http://arxiv.org/abs/math.AG/0112215, 47 pages (Asian J. of Math.,
Vol. 6 (4), December 2002).

\bibitem[V2]{_Verbitsky:LCHK_}
M. Verbitsky,
{\em Vanishing theorems for locally
conformal hyperk{\"a}hler manifolds}, 2003,
http://arxiv.org/abs/math.DG/0302219, 41 pages.

\bibitem[V3]{_Verbitsky_HKT-exa_}
M. Verbitsky,
{\em Hyperkaehler manifolds with torsion obtained from hyperholomorphic bundles}
http://arxiv.org/abs/math.DG/0303129, (Math. Res. Lett. 10 (2003), no. 4, 501--513).

\bibitem[V4]{_Verbitsky:cohe_}
Verbitsky, M., {\em Coherent sheaves on general K3 surfaces and
tori}, http://arxiv.org/abs/math.AG/0205210, 63 pages.

\bibitem[V5]{_Verbitsky:tori_}
Verbitsky, M., {\em Coherent sheaves on generic compact tori},
http://arxiv.org/abs/math.AG/0310329, 24 pages.

\end{thebibliography}