Gorenstein contractions of multiscale differentials (2405.20466v1)

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.