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The seminal work of Eskin-Masur-Zorich described the principal boundary ofmoduli spaces of abelian differentials that parameterizes flat surfaces with aprescribed generic configuration of short parallel saddle connections. In thispaper we describe the principal boundary for each configuration in terms oftwisted differentials over Deligne-Mumford pointed stable curves. We alsodescribe similarly the principal boundary of moduli spaces of quadraticdifferentials originally studied by Masur-Zorich. Our main technique is theflat geometric degeneration and smoothing developed byBainbridge-Chen-Gendron-Grushevsky-M\"{o}ller.

Principal boundary of moduli spaces of abelian and quadratic differentials