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Arithmetically cohen-macaulay curves inP 4 of degree 4 and genus 0

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Abstract

We show that the arithmetically Cohen-Macaulay (ACM) curves of degree 4 and genus 0 in P4 form an irreducible subset of the Hilbert scheme. Using this, we show that the singular locus of the corresponding component of the Hilbert scheme has dimension greater than 6. Moreover, we describe the structures of all ACM curves ofHilb 4m+1 (P4).

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References

  1. J. A. Christophersen,Notes on the component of the rational normal curves in Hilb nt+1, manuscript, 1989.

  2. J. A. Christophersen, pvt. comm.

  3. D. Eisenbud, O. Riemenschneider, F.-O. Schreyer,Projective resolutions of Cohen-Macaulay algebras, Math. Ann.257 (1981), 85–98.

    Article  MATH  Google Scholar 

  4. G. Ellingsrud,Sur le schéma de Hilbert des variétés de codimension 2 dans Pe à cône de Cohen-Macaualay, Ann. scient. Éc. Norm. Sup.8 (1975), 423–432.

    MATH  Google Scholar 

  5. A. Grothendieck,Techniques de construction et théorèmes d’existence en géométrie algébrique IV: Les schémas de Hilbert, Sém. Bourbaki13 (1960/61), exp. 221.

  6. R. Hartshorne,Connectedness of the Hilbert scheme, IHES Publ. Math.29 (1966), 261–309.

    Google Scholar 

  7. R. Hartshorne,Genus of space curves, Ann. Univ. Ferrara Sez. VII (N. S.)40 (1994), 207–223 (1996).

    Google Scholar 

  8. A. Iarrobino,Hilbert scheme of points: Overview of last ten years, Proc. Symp. Pure Math.46 Part 2 (1987), 297–320.

    Google Scholar 

  9. M. Martin-Deschamps, D. Perrin,Sur les bornes des modules de Rao, C.R.Acad.Sc.317 Série 1 (1993), 1158–1162.

    Google Scholar 

  10. Migliore J.,On linking double lines, Trans. A.M.S.294 (1986), 177–185.

    Article  MATH  Google Scholar 

  11. R. Piene, M. Schlessinger,On the Hilbert scheme compactification of the space of twisted cubics, Amer. J. Math.107 (1985), 761–774.

    Article  MATH  Google Scholar 

  12. A. Reeves,Th radius of the Hilbert scheme, J. Algebraic Geometry4 (1995), 639–757.

    MATH  Google Scholar 

  13. G. Sacchiero,Fibrati normali de curve razionali dello spazio proiettivo, Ann. Univ. Ferrara Sez. VII (N. S.)26 (1980), 33–40 (1981).

    Google Scholar 

  14. J. Wahl,Equations defining rational singularities, Ann. scient. Éc. Norm. Sup.10 (1977), 231–264.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques et d’Informatique, École Normale Supérieure, 45 rue d’Ulm, F-75230, Paris Cédex 05, France

    Mireille Martin-Deschamps

  2. Matematisk institutt, Universitetet i Oslo, P.B. 1053 Blindern, N-0316, Oslo, Norway

    Ragni Piene

Authors
  1. Mireille Martin-Deschamps
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  2. Ragni Piene
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Supported in part by the Norwegian Research Council (Matematisk Seminar).

Supported in part by École Normale Supérieure and the Nansen Fund.

This article was processed by the author using the Springer-Verlag TEX PJourlg macro package 1991.

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Martin-Deschamps, M., Piene, R. Arithmetically cohen-macaulay curves inP 4 of degree 4 and genus 0. Manuscripta Math 93, 391–408 (1997). https://doi.org/10.1007/BF02677480

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  • DOI: https://doi.org/10.1007/BF02677480

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