113 research outputs found
Estimates of the number of rational mappings from a fixed variety to varieties of general type
First we find effective bounds for the number of dominant rational maps between two fixed smooth projective varieties with ample
canonical bundles. The bounds are of the type , where , is the canonical bundle of and
are some constants, depending only on . Then we show that for any variety
there exist numbers and with the following properties: For
any threefold of general type the number of dominant rational maps is bounded above by . The number of threefolds , modulo birational
equivalence, for which there exist dominant rational maps , is
bounded above by . If, moreover, is a threefold of general type, we
prove that and only depend on the index of the
canonical model of and on .Comment: A revised version. The presentation of results and proofs has been
improved. AMS-TeX, 19 page
On C-fibrations over projective curves
The goal of this paper is to present a modified version (GML) of ML invariant
which should take into account rulings over a projective base and allow further
stratification of smooth affine rational surfaces. We provide a non-trivial
example where GML invariant is computed for a smooth affine rational surface
admitting no C-actions. We apply GML invariant to computation of ML invariant
of some threefolds.Comment: 21 pages, LaTe
Jordan properties of automorphism groups of certain open algebraic varieties
Let be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that is birational to a product of a smooth projective variety and the projective line. We prove that if contains no rational curves then the automorphism group of is Jordan. That means that there is a positive integer such that every finite subgroup of contains a commutative subgroup such that is normal in and the index
Algorithmic decidability of Engel's property for automaton groups
We consider decidability problems associated with Engel's identity
( for a long enough commutator sequence) in groups
generated by an automaton. We give a partial algorithm that decides, given
, whether an Engel identity is satisfied. It succeeds, importantly, in
proving that Grigorchuk's -group is not Engel. We consider next the problem
of recognizing Engel elements, namely elements such that the map
attracts to . Although this problem seems intractable in
general, we prove that it is decidable for Grigorchuk's group: Engel elements
are precisely those of order at most . Our computations were implemented
using the package FR within the computer algebra system GAP
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
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