Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type

Xia Liao

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Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type

机译：具有线性雅可比理想的自由因数的Chern对数导数类

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摘要

Let X be a nonsingular variety defined over an algebraically closed field of characteristic 0, and D be a free divisor with Jacobian ideal of linear type. We compute the Chern class of the sheaf of logarithmic derivations along D and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement. Our result establishes a conjecture by Aluffi raised in [Alu12b].

机译：令X为在特征为0的代数封闭域上定义的非奇异变量，而D为线性形式雅可比理想的自由除数。我们计算沿D的对数导数的Chern类，并将其与超曲面补子的Chern-Schwartz-MacPherson类进行比较。我们的结果建立了Aluffi在[Alu12b]中提出的猜想。

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来源
《Journal of the Mathematical Society of Japan》 |2018年第3期|975-988|共14页
作者
Xia Liao;
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作者单位

Department of Mathematical Sciences Huaqiao University Chenghua North Road 269 Quanzhou 36201, Fujian, China;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Chern-Schwartz-MacPherson class; logarithmic derivation; Jacobian ideal of linear type;

机译：Chern-Schwartz-MacPherson类;对数推导;线性雅可比理想;

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2. Splayed divisors and their Chern classes [J] . Paolo Aluffi, Eleonore Faber The Journal of the London Mathematical Society . 2013,第2期

机译：张开的除数及其Chern类
3. Borcherds products and Chern classes of Hirzebruch-Zagier divisors [J] . Jan Hendrik Bruinier Inventiones Mathematicae . 1999,第1期

机译：Bircherds产品和Hirzebruch-Zagier除数的Chern类
4. Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements [C] . Graham Denham, Mathias Schulze MSJ-SI . 2012

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5. Three Dimensional Jacobian Derivations And Divisor Class Groups. [D] . Alkarni, Shalan. 2016

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7. Chern Classes of Logarithmic Derivations for Free Divisors with Jacobian Ideal of Linear Type [O] . Liao, Xia 2017

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Chern classes of logarithmic derivations for free divisors with Jacobian ideal of linear type

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