Wednesday, January 9, 2013

1301.1407 (Chih-Chung Liu)

Dynamics of Abelian Vortices Without Common Zeros in the Adiabatic Limit    [PDF]

Chih-Chung Liu
On a smooth line bundle $L$ over a compact K\"ahler surface $\Sigma$, we study vortex equations with a parameter $s$. For each $s$, we invoke techniques in [Br] by turning vortex equations into the elliptic partial differential equations considered in [K-W] to obtain a family of solutions. Our results show that such a family exhibit well controlled convergent behaviors, leading us to prove a conjecture posed by Baptista in [Ba].
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