5,056 research outputs found
Jordan property for non-linear algebraic groups and projective varieties
A century ago, Camille Jordan proved that the complex general linear group
has the Jordan property: there is a Jordan constant such that
every finite subgroup has an abelian subgroup of index
. We show that every connected algebraic group (which is
not necessarily linear) has the Jordan property with the Jordan constant
depending only on , and that the full automorphism group of
every projective variety has the Jordan propertyComment: American Journal of Mathematics (to appear); minor change
Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals
We demonstrate experimentally that the interactions between a pair of
nonlocal spatial optical solitons in a nematic liquid crystal (NLC) can be
controlled by the degree of nonlocality. For a given beam width, the degree of
nonlocality can be modulated by varying the pretilt angle of NLC molecules via
the change of the bias. When the pretilt angle is smaller than pi/4, the
nonlocality is strong enough to guarantee the independence of the interactions
on the phase difference of the solitons. As the pretilt angle increases, the
degree of nonlocality decreases. When the degree is below its critical value,
the two solitons behavior in the way like their local counterpart: the two
in-phase solitons attract and the two out-of-phase solitons repulse.Comment: 3 pages, 4 figure
Structures theorems and applications of non-isomorphic surjective endomorphisms of smooth projective threefolds
Let be a non-isomorphic (i.e., ) surjective
endomorphism of a smooth projective threefold . We prove that any birational
minimal model program becomes -equivariant after iteration, provided that
is -primitive. Here -primitive means that there is no
-equivariant (after iteration) dominant rational map to a positive lower-dimensional projective variety such that the first
dynamical degree remains unchanged. This way, we further determine the building
blocks of . As the first application, we prove the Kawaguchi-Silverman
conjecture for every non-isomorphic surjective endomorphism of a smooth
projective threefold. As the second application, we reduce the Zariski dense
orbit conjecture for to a terminal threefold with only -equivariant Fano
contractions.Comment: 48 pages, comments are welcome
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