790 research outputs found
Moduli space of -holomorphic subvarieties
We study the moduli space of -holomorphic subvarieties in a
-dimensional symplectic manifold. For an arbitrary tamed almost complex
structure, we show that the moduli space of a sphere class is formed by a
family of linear system structures as in algebraic geometry. Among the
applications, we show various uniqueness results of -holomorphic
subvarieties, e.g. for the fiber and exceptional classes in irrational ruled
surfaces. On the other hand, non-uniqueness and other exotic phenomena of
subvarieties in complex rational surfaces are explored. In particular,
connected subvarieties in an exceptional class with higher genus components are
constructed. The moduli space of tori is also discussed, and leads to an
extension of the elliptic curve theory.Comment: 45 pages. v2, presentation improved. v3, Corollary 3.9 adde
Poly(1-vinyl-1,2,4-triazolium) poly(ionic liquid)s: synthesis and the unique behavior in loading metal ions
Herein we report the synthesis of a series of
poly(4-alkyl-1-vinyl-1,2,4-triazolium) poly(ionic liquid)s either via
straightforward free radical polymerization of their corresponding ionic liquid
monomers, or via anion metathesis of the polymer precursors bearing halide as
counter anion. The ionic liquid monomers were first prepared via N-alkylation
reaction of commercially available 1-vinyl-1,2,4-triazole with alkyl iodides,
followed by anion metathesis with targeted fluorinated anions. The thermal
properties and solubilities of these poly(ionic liquid)s have been
systematically investigated. Interestingly, it was found that the
poly(4-ethyl-1-vinyl-1,2,4-triazolium) poly(ionic liquid) exhibited an improved
loading capacity of transition metal ions in comparison with its imidazolium
counterpart.Comment: 18 pages, 9 figure
J-holomorphic curves in a nef class
Taubes established fundamental properties of holomorphic subvarieties in
dimension 4 in \cite{T1}. In this paper, we further investigate properties of
reducible holomorphic subvarieties. We offer an upper bound of the total
genus of a subvariety when the class of the subvariety is nef. For a
spherical class, it has particularly strong consequences. It is shown that, for
any tamed , each irreducible component is a smooth rational curve. We also
completely classify configurations of maximal dimension. To prove these results
we treat subvarieties as weighted graphs and introduce several combinatorial
moves.Comment: 30 pages. v2 Section 4.3 revised; minor changes elsewhere. v3
mistakes correcte
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