稳定曲线映射的变形

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics Pub Date : 2001-12-01 DOI:10.1016/S0764-4442(01)02167-X

Catriona Maclean

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引用次数: 0

摘要

给定一个光滑的变量X和一个映射g:X→Δ，使得g−1(0)是一个正规的交叉变量X0=X1∪ZX2，我们考虑作为映射族中心纤维的稳定映射F0:C0→X0。将这样一个稳定映射分解为F1:C1→X1和F2:C2→X2，我们得到了Chow群A0(F−1i(Z))中0环Ci∩Zi的条件。这些条件为Li和阮在[4]和Gathmann在[2]中的工作提供了基本的几何证明。

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Deformations of stable maps of curves

Given a smooth variety, X and a map g:X→Δ such that g⁻¹(0) is a normal crossing variety X₀=X₁∪_ZX₂, we consider stable maps F₀:C₀→X₀ which appear as the central fibre of a family of maps Splitting such a stable map up into F₁:C₁→X₁ and F₂:C₂→X₂, we derive conditions on the 0-cycle C_i∩Z_i in the Chow group A⁰(F⁻¹_i(Z)). These conditions provide an elementary geometric justification for the work of Li and Ruan in [4] and of Gathmann in [2].

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Comptes Rendus de l'Académie des Sciences - Series I - Mathematics

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