10,264 research outputs found
An application of exceptional bundles to the moduli of stable sheaves on a K3 surface
Let M(v) be the moduli of stable sheaves on K3 surfaces X of Mukai vector v.
If v is primitive, than it is expected that M(v) is deformation equivalent to
some Hilbert scheme and weight two hogde structure can be described by
H^*(X,Z). These are known by Mukai, O'Grady and Huybrechts if rank is 1 or 2,
or the first Chern class is primitive. Under some conditions on the dimension
of M(v), we shall show that these assertion are true. For the proof, we shall
use Huybrechts's results on symplectic manifolds.Comment: 12 pages, AMS-Late
The volume growth of hyperkaehler manifolds of type A_{\infty}
We study the volume growth of hyperkaehler manifolds of type
constructed by Anderson-Kronheimer-LeBrun and Goto. These are noncompact
complete 4-dimensional hyperkaehler manifolds of infinite topological type.
These manifolds have the same topology but the hyperkaehler metrics are depends
on the choice of parameters. By taking a certain parameter, we show that there
exists a hyperkaehler manifold of type whose volume growth is r^a
for each 3<a<4
A note on Fourier-Mukai transform
In this note, we consider the problem on the preservation of stability under
the Fourier-Mukai transforms. We first show that the Fourier-Mukai transform on
an abelian surface or a K3 surface does not always preserve the stability, even
for a -stable vector bundle. We next provide some positive results on this
problem. Finally we discuss the birational map of moduli spaces on an abelian
surface.Comment: 19 pages, some results adde
A note of moduli of vector bundles on rational surfaces
We discuss some relations of moduli of sheaves on rational surfaces by using
universal extensions. These are a generalization of Maruyama's method to
construct Uhlenbeck compactification of moduli of vector bundles.Comment: 11 page
Twisted stability and Fourier-Mukai transform
In this paper, we consider the preservation of stability by using the notion
of Twisted stability. As applications, (1) we show that moduli spaces of vector
bundles on K3 and abelian surfaces are irreducible, (2) we compute Hodge
polynomials of some moduli spaces of vector bundles on Enriques surfaces and on
elliptic surfaces with a section.Comment: 28 page
Construction of a one-dimensional set which asymptotically and omnidirectionally contains arithmetic progressions
In this paper, we construct a subset of which asymptotically
and omnidirectionally contains arithmetic progressions but has Assouad
dimension 1. More precisely, we say that asymptotically and
omnidirectionally contains arithmetic progressions if we can find an arithmetic
progression of length and gap length with direction inside the neighbourhood of for all
, and . Moreover, the dimension of our
constructed example is the lowest-possible because we prove that a subset of
which asymptotically and omnidirectionally contains arithmetic
progressions must have Assouad dimension greater than or equal to 1. We also
get the same results for arithmetic patches, which are the higher dimensional
extension of arithmetic progressions.Comment: 7 page
Liquid Xenon detector R&D for search (KamXP)
The R&D for a new type of liquid xenon (LXe) detector is ongoing to search
for the neutrinoless double-beta decay (). As a result of the
KamLAND-Zen experiment, it is very important to realize the all active region
detector for the energy deposition of the radiation. Newly developed additional
BG reduction techniques will improve the sensitivity of search in
the future. Our detector concept is LXe stored in a new type of plastic
scintillator vessel. The wavelength of LXe scintillation light is shifted to
visible light from 175nm (VUV) on the inner surface of the vessel. Therefore,
the LXe scintillation light can be detected by photon sensors which are far
away from the target nuclei. The pulse shape difference between
LXe and plastic scintillator is used for the additional BG reduction. In the
future, B solar neutrino events will be one of the dominant BGs in
search. To reduce the B solar neutrino BG, the directional
information of the Cherenkov light might be useful. The status of LXe detector
R&D to improve the sensitivity of search is reported.Comment: 4 pages, 6 figures, Proceedings of the 16th International Conference
on Topics in Astroparticle and Underground Physics (TAUP 2019), September
9-13, 2019, Toyama, Japa
Albanese map of moduli of stable sheaves on abelian surfaces
Periods of moduli spaces of stable sheaves on K3 surfaces were computed by
Mukai, O'Grady and the author. In this paper, we shall treat moduli spaces of
stable sheaves on abelian surfaces.Comment: 10 page
The nonuniqueness of the tangent cones at infinity of Ricci-flat manifolds
It is shown by Colding and Minicozzi the uniqueness of the tangent cone at
infinity of Ricci-flat manifolds with Euclidean volume growth which has at
least one tangent cone at infinity with a smooth cross section. In this article
we raise an example of the Ricci-flat manifold implying that the assumption for
the volume growth in the above result is essential. More precisely, we
construct a complete Ricci-flat manifold of dimension 4 with non-Euclidean
volume growth who has at least two distinct tangent cones at infinity and one
of them has a smooth cross section
A fractal proof of the infinitude of primes
This short paper gives another proof of the infinitude of primes by using
upper box dimension, which is one of fractal dimensions.Comment: 4 page
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