Durfee inequalities for quasihomogeneous complete intersections of codimension two

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Contributed by Qiyue Tang ↗

Version 1 / Oct 20, 2026 / CC BY 4.0

Abstract

For positive-weight quasihomogeneous isolated complete intersections of minimal embedding codimension two, we prove μ≥4pg+1\mu\ge4p_g+1 in dimension two and μ>Cn,2pg\mu>C_{n,2}p_g in every dimension n≥3n\ge3.

Provenance statement

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References

  1. G.-M. Greuel and H. A. Hamm, Invarianten quasihomogener vollständiger Durchschnitte , Invent. Math. 49 (1978), 67--86. doi:10.1007/BF01399511 (https://doi.org/10.1007/BF01399511).DOI
  2. M. Morales, Resolution of quasi-homogeneous singularities and plurigenera , Compositio Math. 64 (1987), 311--327. Numdam archive (https://www.numdam.org/item/CM_1987__64_3_311_0/).link
  3. D. Kerner and A. Némethi, The ``corrected Durfee's inequality'' for homogeneous complete intersections , Math. Z. 274 (2013), 1385--1400. doi:10.1007/s00209-012-1120-y (https://doi.org/10.1007/s00209-012-1120-y).DOI
  4. D. Kerner and A. Némethi, Durfee-type bound for some non-degenerate complete intersection singularities , Math. Z. 285 (2017), 159--175. doi:10.1007/s00209-016-1702-1 (https://doi.org/10.1007/s00209-016-1702-1).DOI
  5. R. Hartshorne, Residues and Duality , Lecture Notes in Mathematics, vol. 20, Springer-Verlag, Berlin, 1966. doi:10.1007/BFb0080482 (https://doi.org/10.1007/BFb0080482).DOI
  6. H. Grauert and O. Riemenschneider, Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen , Invent. Math. 11 (1970), 263--292 (https://doi.org/10.1007/BF01403182).DOI

Version history

  1. v1Submitted by Qiyue TangInitial depositCurrentOct 18, 2026