Modular compactifications of the space of pointed elliptic curves I
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 6 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 M1,n(m). We also consider weighted variants of these stability conditions, and construct the corresponding...[Show more]
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