The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.
Moduli of Singular Curves
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abstract
The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also prove the boundedness of the open substack of U parameterizing geometrically connected curves with fixed arithmetic genus g and $\leq$ e irreducible components. This is an updated and expanded version of [arXiv:0902.3690v2, Appendix B].
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Properties of deformed mass and phase functions
The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.