Alper, Jarod; Fedorchuk, Maksym; Smyth, David; van der Wyck, Frederick
This is the first of three papers in which we give a moduli interpretation of the second flip in the log minimal model program for , replacing the locus of curves with a genus Weierstrass tail by a locus of curves with a ramphoid cusp. In this paper, for , we introduce new -stability conditions for curves and prove that they are deformation open. This yields algebraic stacks related by open immersions . We prove that around a curve corresponding to a closed point in , these open immersions are...[Show more]
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