48,342 research outputs found
An example on deformation of a pair
In this paper we give an example to show Clemens' conjecture is not a first
order deformation problem
Perturbations around black holes
Perturbations around black holes have been an intriguing topic in the last
few decades. They are particularly important today, since they relate to the
gravitational wave observations which may provide the unique fingerprint of
black holes' existence. Besides the astrophysical interest, theoretically
perturbations around black holes can be used as testing grounds to examine the
proposed AdS/CFT and dS/CFT correspondence.Comment: 14 pages, 4 figures, Invited plenary talk given in the Conference
"100 Years of Relativity", Sao Paulo, Brazil, August 200
Rational curves on hypersurfaces
In this paper, we prove three related results;
(1) Extension of our result in [10] to all generic hypersurfaces. More
precisely, the normal sheaf of a generic rational map to a generic
hypersurface of has a vanishing higher cohomology,
\begin{equation} H^1(N_{c_0/X_0})=0. \end{equation}
As applications we give
(2) A solution to a Voisin's conjecture [9] on a covering of a generic
hypersurface by rational curves
(3) A classification of rational curves on hypersurfaces of general type--a
solution to another Voisin's conjecture [9].Comment: arXiv admin note: substantial text overlap with arXiv:1202.283
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