4,448 research outputs found
Invariance of Plurigenera
The following conjecture on the deformation invariance of plurigenera is
proved. For a smooth projective holomorphic family of compact complex manifolds
over the open unit 1-disk such that all the fibers are of general type, every
plurigenus of the fiber is independent of the fiber.
The proof uses Nadel's multiplier ideal sheaves, Skoda's result on the
generation of ideals with L2 estimates with respect to a plurisubharmonic
weight, and the extension theorem of Ohsawa-Takegoshi-Manivel for holomorphic
top-degree forms which are L2 with respect to a plurisubharmonic weight.Comment: 13 pages, LaTeX fil
Abundance conjecture
We sketch a proof of the abundance conjecture that the Kodaira dimension of a
compact complex algebraic manifold equals its numerical Kodaira dimension. The
proof consists of the following three parts: (i) the case of numerical Kodaira
dimension zero, (ii) the general case under the assumption of the coincidence
of the numerically trivial foliation and fibration for the canonical bundle,
and (iii) the verification of the coincidence of the numerically trivial
foliation and fibration for the canonical bundle. Besides the use of standard
techniques such as the L2 estimates of d-bar, the first part uses Simpson's
method of replacing the flat line bundle in a nontrivial flatly twisted
canonical section by a torsion flat line bundle. Simpson's method relies on the
technique of Gelfond-Schneider for the solution of the seventh problem of
Hilbert. The second part uses the semi-positivity of the direct image of a
relative pluricanonical bundle. The third part uses the technique of the First
Main Theorem of Nevanlinna theory and its use is related to the technique of
Gelfond-Schneider in the first part
Maximally Flexible Assignment of Orthogonal Variable Spreading Factor Codes for Multi-Rate Traffic
In universal terrestrial radio access (UTRA) systems, orthogonal variable spreading factor (OVSF) codes are used to support different transmission rates for different users. In this paper, we first define the flexibility index to measure the capability of an assignable code set in supporting multirate traffic classes. Based on this index, two single-code assignment schemes, nonrearrangeable and rearrangeable compact assignments, are proposed. Both schemes can offer maximal flexibility for the resulting code tree after each code assignment. We then present an analytical model and derive the call blocking probability, system throughput and fairness index. Analytical and simulation results show that the proposed schemes are efficient, stable and fair
Delay distributions of slotted ALOHA and CSMA
We derive the closed-form delay distributions of slotted ALOHA and nonpersistent carrier sense multiple access (CSMA) protocols under steady state. Three retransmission policies are analyzed. We find that under a binary exponential backoff retransmission policy, finite average delay and finite delay variance can be guaranteed for G<2S and G<4S/3, respectively, where G is the channel traffic and S is the channel throughput. As an example, in slotted ALOHA, S<(ln2)/2 and S<3(ln4-ln3)/4 are the operating ranges for finite first and second delay moments. In addition, the blocking probability and delay performance as a function of r/sub max/ (maximum number of retransmissions allowed) is also derived
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