摘要翻译:
研究了任意维数基上一族节点(或光滑)曲线的相对Hilbert格式,通过它的(双分)圈映射,得到相对对称积。我们证明了循环映射是判别轨迹的爆破,判别轨迹是由多个点的循环组成的。我们研究了在希尔伯特格式中的一些自然循环,包括广义对角线和循环,称为“节点滚动”,支持在奇异点上的参数化格式中的爆破或“判别”极化的作用。本文给出了与枚举几何密切相关的重言向量丛Chern类的交积分。
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英文标题:
《Geometry and intersection theory on Hilbert schemes of families of nodal
curves》
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作者:
Ziv Ran
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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 study the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension, via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the discriminant locus, which consists of cycles with multiple points. We work out the action of the blowup or 'discriminant' polarization on some natural cycles in the Hilbert scheme, including generalized diagonals and cycles, called 'node scrolls', parametrizing schemes supported on singular points. We derive an intersection calculus for Chern classes of tautological vector bundles, which are closely related to enumerative geometry.
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PDF链接:
https://arxiv.org/pdf/0803.4512