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- W2891359197 abstract "We prove a convergence result for a family of Yang-Mills connections over an elliptic $K3$ surface $M$ as the fibers collapse. In particular, assume $M$ is projective, admits a section, and has singular fibers of Kodaira type $I_1$ and type $II$. Let $Xi_{t_k}$ be a sequence of $SU(n)$ connections on a principal $SU(n)$ bundle over $M$, that are anti-self-dual with respect to a sequence of Ricci flat metrics collapsing the fibers of $M$. Given certain non-degeneracy assumptions on the spectral covers induced by $barpartial_{Xi_{t_k}}$, we show that away from a finite number of fibers, the curvature $F_{Xi_{t_k}}$ is locally bounded in $C^0$, the connections converge along a subsequence (and modulo unitary gauge change) in $L^p_1$ to a limiting $L^p_1$ connection $Xi_0$, and the restriction of $Xi_0$ to any fiber is $C^{1,alpha}$ gauge equivalent to a flat connection with holomorphic structure determined by the sequence of spectral covers. Additionally, we relate the connections $Xi_{t_k}$ to a converging family of special Lagrangian multi-sections in the mirror HyperKahler structure, addressing a conjecture of Fukaya in this setting." @default.
- W2891359197 created "2018-09-27" @default.
- W2891359197 creator A5003119957 @default.
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- W2891359197 date "2018-09-23" @default.
- W2891359197 modified "2023-09-23" @default.
- W2891359197 title "Adiabatic limits of anti-self-dual connections on collapsed K3 surfaces" @default.
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- W2891359197 doi "https://doi.org/10.48550/arxiv.1809.08583" @default.
- W2891359197 hasPublicationYear "2018" @default.
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