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On the Existence of Maximal Rank Curves with Prescribed Hartshorne-Rao Module

  • Silvio Greco
  • Rosa Maria Miró-Roig
Part of the Progress in Mathematics book series (PM, volume 280)

Abstract

In this paper, we study maximal rank curves C ⊂ ℙ3 in connection to their cohomology and natural lifting properties. More precisely, we set R = K[x, y, z, t] and we address the following 4 problems:
  1. (1)

    To characterize the graded finite length R-modules M such that there is a maximal rank curve in the biliaison class of M.

     
  2. (2)

    To characterize the graded finite length R-modules M such that there is a maximal rank curve C in the biliaison class of M with the lifting property s(C) = σ(C).

     
  3. (3)

    To characterize the graded finite length R-modules M such that there is a maximal rank curve C in the biliaison class of M with the lifting property s(C) = σ*(C).

     
  4. (4)

    To characterize the Rao functions of the maximal rank curves C, with the lifting property s(C) = σ(C) (resp. s(C) = σ*(C)). We partially answer the problems (1)–(3). Problem (4) seems to be more difficult and we can only describe some classes of Rao functions associated to some maximal rank curves.

     

Mathematics Subject Classification (2000)

14H50 

Keywords

Hartshorne-Rao module Maximal Rank curves Liaison theory biliaison Buchsbaum index lifting properties 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Silvio Greco
    • 1
  • Rosa Maria Miró-Roig
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  2. 2.Departament d’Algebra i GeometriaFacultat de MatemàtiquesBarcelonaSpain

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