CLASSIFICATION OF QUASIHOMOGENEOUS POLYNOMIALS WITH INNER MODALITY=ARITHMETIC INNER MODALITY

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For quasihomogeneous polynomials with isolated sin-gularity, V.I.Arnold introduced the notion of inner modality and classified them with inner modality =0,1 in [1]. After that, E. Yoshinaga, M. Suzuki, J. Estrada Sarlabous, J. Arocha and A. Fuentes classified them with inner modality ≤9 (see [18],[11],[7],[15]). The author introduced a concept of arithmetic inner modal-ity for quasihomogeneous polynomials with isolated singularity in [15], and he observed that these two invariants match each other for quasihomogeneous polynomials with inner modality ≤9, and also he found examples with inner modality = 10 for which two invariants don’t match (see [14]). We are interested in how many quasihomogeneous polynomials with the same inner modality as arithmetic inner modality. The purpose of this paper is to give the complete classification of quasihomogeneous polynomials with the same inner modality as arithmetic inner modality.

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  • 研究紀要

    研究紀要 55 219-242, 2020-03-05

    日本大学文理学部自然科学研究所

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