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NATURE'S ETERNAL FASCISM
Написал экзегезис на научные темы,
для отчетности разумеется. За последние полгода примерно.

http://arxiv.org/abs/math.AG/0310329
Found a new kind of twistor space, associated with complex
tori. Using a version of Ward correspondence, shown that
the category of coherent sheaves on a generic compact
complex torus of dimension $\geq 2$ is independent
from the choice of complex structure. This was
proven earlier for even-dimensional tori, using
the hyperkaehler structures.

http://arxiv.org/abs/math.AG/0312520
Found an easy and conceptual proof of an old result
showing that any complex submanifold of a hyperkaehler
manifold, taken with respect to a generic complex
structure induced by the hyperkaehler structure,
is complex analytic with respect to all induced
complex structures. The earlier proof relied on Hodge
structures, while the new one is elementary and
works for non-compact manifolds.

http://arxiv.org/abs/math.AG/0403430
Discovered striking new results on holomorphic vector
bundles on principal elliptic fibrations. It was found that
the geometry of principal elliptic fibrations in dimension
bigger than 2 is very much different from that in dimension
2 (which is well studied). Introduced a new notion of positive
principal elliptic fibration, which is a fibration $M$ over
a Kaehler base $X$, such that the Kaehler form on $X$ lifted
to $M$ becomes exact. Many principal elliptic fibrations
studied in the literature are positive (in particular,
the Hopf manifolds, the regular Vaismann manifolds,
the Calabi-Eckmann manifolds are positive). Discovered
many important results about positive principal elliptic
fibrations. It was shown that any stable bundle on a
positive principal elliptic fibration $M$ ($\dim M >2$)
is lifted from the base, up to a twist by a line bundle.
This implies also that any coherent sheaf on a positive
principal elliptic fibration is filtered by coherent
sheaves of rank 1.


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