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