8,243 research outputs found
Characteristic Classes of Bad Orbifold Vector Bundles
We show that every bad orbifold vector bundle can be realized as the
restriction of a good orbifold vector bundle to a suborbifold of the base
space. We give an explicit construction of this result in which the Chen-Ruan
orbifold cohomology of the two base spaces are isomorphic (as additive groups).
This construction is used to indicate an extension of the Chern-Weil
construction of characteristic classes to bad orbifold vector bundles. In
particular, we apply this construction to the orbifold Euler class and
demonstrate that it acts as an obstruction to the existence of nonvanishing
sections.Comment: 12 pages; improved expositio
A novel multi-component generalization of the short pulse equation and its multisoliton solutions
We propose a novel multi-component system of nonlinear equations that
generalizes the short pulse (SP) equation describing the propagation of
ultra-short pulses in optical fibers. By means of the bilinear formalism
combined with a hodograph transformation, we obtain its multi-soliton solutions
in the form of a parametric representation. Notably, unlike the determinantal
solutions of the SP equation, the proposed system is found to exhibit solutions
expressed in terms of pfaffians. The proof of the solutions is performed within
the framework of an elementary theory of determinants. The reduced 2-component
system deserves a special consideration. In particular, we show by establishing
a Lax pair that the system is completely integrable. The properties of
solutions such as loop solitons and breathers are investigated in detail,
confirming their solitonic behavior. A variant of the 2-component system is
also discussed with its multisoliton solutions.Comment: Minor correction
Tate twists of Hodge structures arising from abelian varieties of type IV
We show that certain abelian varieties A have the property that for every
Hodge structure V in the cohomology of A, every effective Tate twist of V
occurs in the cohomology of some abelian variety. We deduce the general Hodge
conjecture for certain non-simple abelian varieties of type IV
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