Abstract
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 locally modeled by variation of geometric invariant theory for the action of on the first-order deformation space of C.
Original language | English |
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Pages (from-to) | 1547-1583 |
Number of pages | 37 |
Journal | Compositio Mathematica |
Volume | 153 |
Issue number | 8 |
DOIs | |
Publication status | Published - 1 Aug 2017 |