来自 Secondary Fan 的热带不变量
代数几何
2012-06-18 v3 组合数学
摘要
本文考虑经过特定数目一般点、具有特定组合类型的热带平面曲线的加权计数。我们给出一个由 secondary fan 上的热带相交理论导出的判别准则，用于判断某加权计数是否给出点位置的不变量。通过计算某相交重数，我们说明 Mikhalkin 计算 Gromov-Witten 不变量的方法如何纳入我们的框架。这开始回应 Dickenstein、Feichtner 和 Sturmfels 提出的一个问题。我们还对所得数值给出涉及 Chow 商的几何解释，并给出一个反例说明热带 Severi 簇并不总是由 secondary fan 支撑。本文是预印本“The Tropical Degree of Cones in the Secondary Fan”的修订版。
引用
@article{arxiv.math/0604290,
title = {Tropical Invariants from the Secondary Fan},
author = {Eric Katz},
journal= {arXiv preprint arXiv:math/0604290},
year = {2012}
}
备注
The paper has been withdrawn by the author due to an error in the proof of Prop 8.17 which can best be called an abuse of homological algebra. Much thanks to Jihyeon Jessie Yang for spotting the error. Section 9 (the geometric interpretation) and section 10 (counterexample regarding the tropical Severi variety) are to the best of the author's knowledge, still correct