Moduli of Singular Curves

Details Moduli of Singular Curves Moduli of Singular Curves

2010-11-28

arxiv.org/abs/1011.6007v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

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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