Gorenstein contractions of multiscale differentials
arxiv(2024)
Abstract
Multiscale differentials arise as limits of holomorphic differentials with
prescribed orders of zeros on nodal curves. In this paper, we address the
conjecture concerning Gorenstein contractions of multiscale differentials,
initially proposed by Ranganathan and Wise and further elaborated upon by
Battistella and Bozlee. Specifically, we show that multiscale differentials can
be contracted into Gorenstein singularities level by level from the top down.
At each level, these differentials can descend to become generators of the
dualizing bundle at the singularities. Additionally, the global residue
condition, which governs the smoothability of multiscale differentials, is a
special case of the residue condition for descent differentials.
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