Misha Verbitsky (tiphareth) wrote,@ 2004-04-12 20:52:00 |

Current mood: | tired |

Current music: | Aavikko - DEREK! |

**NATURE'S ETERNAL FASCISM**

Написал экзегезис на научные темы,

для отчетности разумеется. За последние полгода примерно.

http://arxiv.org/abs/math.AG/031032

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/031252

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/040343

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.

А вот между тем картина: NATURE'S ETERNAL FASCISM

NATURE'S ETERNAL FASCISM

Так что вот

Привет

offtopic satory66
2004-04-12 10:48 (link) | |

Спасибо за замечательную картинку. |

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