106,239 research outputs found
Automorphisms of finite order on Gorenstein del Pezzo surfaces
In this note we shall determine all actions of groups of prime order p with p
> 3 on Gorenstein del Pezzo (singular) surfaces Y of Picard number 1. We show
that every order-p element in Aut(Y) (= Aut(Y'), Y' being the minimal
resolution of Y) is lifted from a projective transformation of the projective
plane. We also determine when Aut(Y) is finite in terms of the self
intersection of the canonical divisor of Y, Sing(Y) and the number of singular
members in the anti-canonical linear system of Y. In particular, we show that
either |Aut(Y)| = 2^a 3^b for some 0 3 there
is at least one element g_p of order p in Aut(Y) (hence |Aut(Y)| is infinite).Comment: 18 pages, Transactions of the American Mathematical Society, to
appea
On the complete classification of extremal log Enriques surfaces
We show that there are exactly, up to isomorphisms, seven extremal log
Enriques surfaces Z and construct all of them; among them types D_{19} and
A_{19} have been shown of certain uniqueness by M. Reid. We also prove that the
(degree 3 or 2) canonical covering of each of these seven Z has either X_3 or
X_4 as its minimal resolution. Here X_3 (resp. X_4) is the unique K3 surface
with Picard number 20 and discriminant 3 (resp. 4), which are called the most
algebraic K3 surfaces by Vinberg and have infinite automorphism groups (by
Shioda-Inose and Vinberg).Comment: 22 pages. Math. Z. to appea
Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces
We present a complete list of extremal elliptic K3 surfaces. There are
altogether 325 of them. The first 112 coincides with Miranda-Persson's list for
semi-stable ones. The data include the transcendental lattice which determines
uniquely the K3 surface by a result of Shioda and Inose, the singular fibre
type and the Mordell Weil group. As an application, we give a sufficient
condition for the topological fundamental group of complement to an
ADE-configuration of smooth rational curves on a K3 surface to be trivial.Comment: 25 pages, Nagoya Math. J. to appea
On cost-effective communication network designing
How to efficiently design a communication network is a paramount task for
network designing and engineering. It is, however, not a single objective
optimization process as perceived by most previous researches, i.e., to
maximize its transmission capacity, but a multi-objective optimization process,
with lowering its cost to be another important objective. These two objectives
are often contradictive in that optimizing one objective may deteriorate the
other. After a deep investigation of the impact that network topology, node
capability scheme and routing algorithm as well as their interplays have on the
two objectives, this letter presents a systematic approach to achieve a
cost-effective design by carefully choosing the three designing aspects. Only
when routing algorithm and node capability scheme are elegantly chosen can
BA-like scale-free networks have the potential of achieving good tradeoff
between the two objectives. Random networks, on the other hand, have the
built-in character for a cost-effective design, especially when other aspects
cannot be determined beforehand.Comment: 6 pages, 4 figure
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