We investigate one-parameter deformations of functions on affine space which define parameterizable hypersurfaces. With the assumption of isolated polar activity at the origin, we are able to completely express the Lê numbers of the special fiber in terms of the Lê numbers of the generic fiber and the characteristic polar multiplicities of the comparison complex, a perverse sheaf naturally associated to any reduced complex analytic space on which the constant sheaf ℚ X • [dimX] is perverse. This generalizes the classical formula for the Milnor number of a plane curve in terms of double points as well as Mond's image Milnor number. We also recover results of Gaffney and Bobadilla using this framework. We obtain similar deformation formulas for maps from ℂ 2 to ℂ 3 , and provide an ansatz for obtaining deformation formulas for all dimensions within Mather's nice dimensions.

Brian Hepler

Annales de l’institut Fourier

ANNALES DE L'INSTITUT FOURIER 旨在发表所有数学领域的高水平原创论文，无论是英文还是法文。编辑委员会鼓励提交包含原创和重要结果的文章，或提出新的证明数学领域的核心成果。此外，ANNALES DE L'INSTITUT FOURIER 是一本通用期刊，高度专业化的文章只有在其阐述能够让更多读者接触到的情况下才能被接受。

The Annales de l'Institut Fourier aims to publish high-quality original papers in all areas of mathematics, accepting submissions in both English and French. The editorial board encourages the submission of articles that contain original and significant results, or that provide new proofs of core results in the field of mathematics. Furthermore, the Annales de l'Institut Fourier is a general journal, and highly specialized articles will only be accepted if they can be presented in a way that makes them accessible to a broader audience.

《Annales de l'Institut Fourier》旨在发表所有数学领域的高水平原创论文，接受英文和法文稿件。编辑委员会鼓励提交包含原创性和重要性结果的文章，或提出新的证明以支持数学领域的核心成果。此外，《Annales de l'Institut Fourier》是一份通用期刊，只有在高度专业化的文章能够以易于理解的方式向更广泛的读者群体阐述时，才会被接受。

Category	Quartile
数学	4
数学, 数学	4

Deformation Formulas for Parameterized Hypersurfaces

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