Moduli of Singular Curves

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 $\le$ e irreducible components. This is an updated and expanded version of [arXiv:0902.3690v2, Appendix B].

11 pages

References in corpus (3)

• Quotients by finite equivalence relations
• The Stack of Rational Nodal Curves
• Families of rationally simply connected varieties over surfaces and torsors for semisimple groups