摘要翻译:
我们比较了在$d=3$时,亏格0稳定映射的Kontsevich模空间与射影空间和拟映射空间。更确切地说,我们证明了当$d=3$时,从准映射空间到稳定映射模空间的明显双形映射是三个爆破后两个爆破的组合。此外,我们根据低阶模空间明确地识别了爆破/下降中心。利用这一点,我们计算了Betti数、积分Picard群和有理上同调环。二度的情况是作为热身进行的。
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英文标题:
《Moduli space of stable maps to projective space via GIT》
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作者:
Young-Hoon Kiem and Han-Bom Moon
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最新提交年份:
2008
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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 compare the Kontsevich moduli space of genus 0 stable maps to projective space with the quasi-map space when $d=3$. More precisely, we prove that when $d=3$, the obvious birational map from the quasi-map space to the moduli space of stable maps is the composition of three blow-ups followed by two blow-downs. Furthermore, we identify the blow-up/down centers explicitly in terms of the moduli spaces for lower degrees. Using this, we calculate the Betti numbers, the integral Picard group, and the rational cohomology ring. The degree two case is worked out as a warm-up.
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PDF链接:
https://arxiv.org/pdf/0711.4929