摘要翻译:
引入孤立曲线奇点序列、椭圆M-折叠点序列和相关的稳定性条件序列,推广了Deligne-Mumford稳定性的一般定义。对于每对0<m<n的整数,我们证明了算术亏格1的n点m-稳定曲线的模问题是可由一个适当的不可约Deligne-Mumford栈表示的。我们还考虑了这些稳定性条件的加权变体,并构造了相应的模栈。在以后的工作中,我们将证明这些栈具有射影粗模,并利用由此得到的空间给出M_{1,n}的对数极小模型程序的完整描述。
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英文标题:
《Modular compactifications of M_{1,n}》
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作者:
David Ishii Smyth
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最新提交年份:
2009
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
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}.
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PDF链接:
https://arxiv.org/pdf/0808.0177