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A Remark on Two Notions of Order of Contact

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Abstract

We recall two measurements of the order of contact of an ideal in the ring of germs of holomorphic functions at a point, and we provide a class of examples in which they differ.

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References

  1. Brinzanescu, V., Nicoara, A.: On the relationship between D’Angelo \(q\)-type and Catlin \(q\)-type. J. Geom. Anal. 25(3), 1701–1719 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brinzanescu, V., Nicoara, A.: Relating Catlin and D’Angelo \(q\)-types, arXiv:1707.08294 [math.DS]

  3. Catlin, D.: Subelliptic estimates for the \(\bar{\partial }\)-Neumann problem on pseudoconvex domains. Ann. Math. 126(1), 131–191 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  4. D’Angelo, J.P.: Subelliptic estimates and failure of semicontinuity for orders of contact. Duke Math. J. 47, 955–957 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  5. D’Angelo, J.P.: Real hypersurfaces, orders of contact, and applications. Ann. Math. 115(3), 615–637 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  6. D’Angelo, J.P.: Several complex variables and the geometry of real hypersurfaces. CRC Press, Boca Raton (1993)

    MATH  Google Scholar 

  7. D’Angelo, J.P., Kohn, J.J.: Subelliptic estimates and finite type. In: Several Complex Variables, Math. Sci. Res. Inst. Publ., vol. 37, Cambridge University Press, Cambridge, pp. 199–232 (1999)

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Acknowledgements

This research was partially supported by NSF Grant DMS 13-61001 of John D’Angelo. The author would like to thank Professor D’Angelo for his support and guidance. The author also wishes to thank the anonymous referees for helpful suggestions. During the revision process of this paper, the author received from Nicoara the preprint [2], which acknowledges this work and corrects [1].

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Correspondence to Martino Fassina.

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Fassina, M. A Remark on Two Notions of Order of Contact. J Geom Anal 29, 707–716 (2019). https://doi.org/10.1007/s12220-018-0015-5

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  • DOI: https://doi.org/10.1007/s12220-018-0015-5

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