Modular compactifications of M_{1,n}

Abstract

We introduce a sequence of isolated curve singularities, the elliptic m-fold points, and an associated sequence of stability conditions, generalizing the usual definition of Deligne-Mumford stability. For every pair of integers 0<m<n, we prove that the moduli problem of n-pointed m-stable curves of arithmetic genus one is representable by a proper irreducible Deligne-Mumford stack. We also consider weighted variants of these stability conditions, and construct the corresponding moduli stacks. In forthcoming work, we will prove that these stacks have projective coarse moduli and use the resulting spaces to give a complete description of the log minimal model program for M_{1,n}.

44 pages, 6 figures; now incorporates weighted variants of stability conditions

References in corpus (2)

• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• Log minimal model program for the moduli space of stable curves of genus three

Cited by in corpus (9)

• Alternate Compactifications of Moduli Spaces of Curves
• Towards a classification of modular compactifications of the moduli space of curves
• Ample divisors on moduli spaces of weighted pointed rational curves, with applications to log MMP for ${\bar{M}}_{0,n}$
• GIT Constructions of Moduli Spaces of Stable Curves and Maps
• Groebner techniques for low degree Hilbert stability
• Towards Mori's program for the moduli space of stable maps
• Log canonical models for ${\bar{M}}_{g,n}$
• Comparison of two desingularization of the Kontsevich's moduli space of elliptic stable maps
• Alternate compactifications of the moduli space of genus one maps