希尔兹布吕赫曲面中的无障碍嵌入

IF 0.6 3区 数学 Q3 MATHEMATICS
Nicki Magill
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引用次数: 0

摘要

本文继续研究交错希尔泽布鲁赫曲面的椭圆嵌入函数,其参数为交错炸开的大小 $b \ in (0, 1)$。Cristofaro-Gardiner 等人$\href{https://doi.org/10.48550/arXiv.2004.13062}{\textrm{arXiv:2004.13062}}$发现,如果希尔兹布鲁赫曲面的嵌入函数有一个无限的阶梯,那么该函数等于阶梯堆积点处的体积曲线。在这里,我们利用几乎环状纤维来构建无限递归定义的无理 $b$ 值系列的堆积点全填充,这意味着这些 $b$ 值是潜在的阶梯值。b$值是通过马吉尔-麦克杜夫-韦勒(Magill-McDuff-Weiler,arXiv:2203.06453)中定义的阻塞类族定义的。阻碍类的递归交织结构与几乎环状纤维的可能突变序列之间存在对应关系。Magill-McDuff-Weiler $\href{ https://ui.adsabs.harvard.edu/link_gateway/2022arXiv220306453M/doi:10.48550/arXiv.2203.06453}{\textrm{(arXiv:2203.06453)}}$中使用了这一结果来证明这些类是例外的,而且这些$b$值确实有无限的阶梯。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unobstructed embeddings in Hirzebruch surfaces
This paper continues the study of the ellipsoid embedding function of symplectic Hirzebruch surfaces parametrized by $b \in (0, 1)$, the size of the symplectic blowup. Cristofaro–Gardiner, et al. $\href{https://doi.org/10.48550/arXiv.2004.13062}{\textrm{arXiv:2004.13062}}$ found that if the embedding function for a Hirzebruch surface has an infinite staircase, then the function is equal to the volume curve at the accumulation point of the staircase. Here, we use almost toric fibrations to construct full-fillings at the accumulation points for an infinite family of recursively defined irrational $b$-values implying these $b$ are potential staircase values. The $b$-values are defined via a family of obstructive classes defined in Magill–McDuff–Weiler (arXiv:2203.06453). There is a correspondence between the recursive, interwoven structure of the obstructive classes and the sequence of possible mutations in the almost toric fibrations. This result is used in Magill–McDuff–Weiler $\href{ https://ui.adsabs.harvard.edu/link_gateway/2022arXiv220306453M/doi:10.48550/arXiv.2203.06453}{\textrm{(arXiv:2203.06453)}}$ to show that these classes are exceptional and that these $b$-values do have infinite staircases.
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: Publishes high quality papers on all aspects of symplectic geometry, with its deep roots in mathematics, going back to Huygens’ study of optics and to the Hamilton Jacobi formulation of mechanics. Nearly all branches of mathematics are treated, including many parts of dynamical systems, representation theory, combinatorics, packing problems, algebraic geometry, and differential topology.
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