Modular compactifications of the space of pointed elliptic curves I

作者：Smyth David Ishii^*

来源：Compositio Mathematica, 2011, 147(3): 877-913.

DOI：10.1112/S0010437X10005014

• moduli of curves
• elliptic curves
• singularities

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 1 <= m < n, we prove that the moduli problem of n-pointed rn-stable curves of arithmetic genus one is representable by a proper irreducible Deligne-Murnford stack <(M)over bar>(1,n)(m). We also consider weighted variants of these stability conditions, and construct the corresponding moduli stacks (M) over bar (1,A)(m). 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) over bar (1,n).

• 出版日期2011-5