Report
Whitney equisingularity of families of surfaces in $\mathbb{C}^3$
| العنوان: | Whitney equisingularity of families of surfaces in $\mathbb{C}^3$ |
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| المؤلفون: | Ruas, M. A. S., Silva, O. N. |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables |
| الوصف: | In this work, we study families of singular surfaces in $\mathbb{C}^3$ parametrized by $\mathcal{A}$-finitely determined map germs. We consider the topological triviality and Whitney equisingularity of an unfolding $F$ of a finitely determined map germ $f:(\mathbb{C}^2,0)\rightarrow(\mathbb{C}^3,0)$. We investigate the following conjecture: topological triviality implies Whitney equisingularity of the unfolding $F$? We provide a complete answer to this conjecture, given counterexamples showing how the conjecture can be false. Comment: 15 pages, 2 figures. Changes in version 2: the proof of Corollary 5.13 of version 1 was not corrected. In version 2, we present counterexamples for the result stated in version 1 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1608.08290 |
| رقم الانضمام: | edsarx.1608.08290 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |