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We study hyperkahler metrics and hyperholomorphic connections of Hitchin'smoduli spaces after Gaiotto, Moore and Neitzke. Their construction via thetwistor technique produces intricate wall crossing behaviors. For certain fourdimensional Hitchin's moduli spaces local models and degeneration to localmodels near singular fibers of the Hitchin's fibration are understood.

SYZ Mirror Symmetry of Hitchin's Moduli Spaces Near Singular Fibers I