Liaison and Cohen–Macaulayness conditions

• Autores: Francesca Cioffi, Roberta Di Gennaro
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 2, 2011, págs. 173-186
• Idioma: inglés
• DOI: 10.1007/s13348-010-0010-z
• Texto completo no disponible (Saber más ...)
• Resumen

  • Using liaison, we study projective curves which are close to complete intersections in terms of Castelnuovo–Mumford regularity or degree and we obtain conditions for a space curve C being arithmetically Cohen–Macaulay, generalizing a result of E. D. Davis. These conditions apply also, in weaker forms, to equidimensional and lCM subschemes of codimension two and to curves in {\mathbb P^n} , with n ≥ 4. The results for curves are sharp as suitable examples show.

• Referencias bibliográficas
  • Bolondi G., Miró-Roig R.M.: Two-codimensional Buchsbaum subschemes of P n via their hyperplane sections. Comm. Algebra 17(8), 1989–2016 (1989)
  • Brodmann M., Nagel U.: Bounding cohomological Hilbert functions by hyperplane sections. J. Algebra 174(1), 323–348 (1995)
  • Cioffi F., Marinari M.G., Ramella L.: Regularity bounds by minimal generators and Hilbert function. Collect. Math. 60(1), 89–100 (2009)
  • CoCoATeam, CoCoA: a system for doing Computations in Commutative Algebra. Available at http://cocoa.dima.unige.it
  • Davis, E.D.: Curves which are close to complete intersections, The Curves Seminar at Queen’s, Vol. VII (Kingston, ON, 1990), Queen’s Papers...
  • Davis E.D., Geramita A.V., Maroscia P.: Perfect homogeneous ideals: Dubreil’s theorems revisited. Bull. Sci. Math. (2) 108(2), 143–185 (1984)
  • Davis E.D., Geramita A.V., Orecchia F.: Gorenstein algebras and the Cayley–Bacharach theorem. Proc. Am. Math. Soc. 93(4), 593–597 (1985)
  • Di Gennaro R., Nagel U.: The equations of space curves on a quadric. Collect. Math. 58(1), 119–130 (2007)
  • Greco, S.: Normal varieties, Institutiones Mathematicae [Mathematical Methods], IV, Academic Press Inc. [Harcourt Brace Jovanovich Publishers],...
  • Gruson, L., Peskine, C.: Genre des courbes de l’espace projectif, Algebraic geometry (Proc. Sympos., Univ. Tromsø Tromsø 1977). Lecture Notes...
  • Hartshorne, R.: Algebraic geometry. Graduate Text in Mathematics, vol. 52. Springer, New York (1977)
  • Hartshorne R.: The genus of space curves. Ann. Univ. Ferrara Sez. VII (N.S.) 40(1994), 207–223 (1996)
  • Hartshorne, R., Schlesinger, E.: Curves in the double plane. Comm. Algebra 28(12), 5655–5676 (2000), Special issue in honor of Robin Hartshorne
  • Huneke C., Ulrich B.: General hyperplane sections of algebraic varieties. J. Algebraic Geom. 2(3), 487–505 (1993)
  • Kunz, E.: Introduction to commutative algebra and algebraic geometry. Birkhäuser Boston Inc., Boston, MA (1985). Translated from the German...
  • Martin H.M., Migliore J.C., Nollet S.: Degrees of generators of ideals defining curves in projective space. Comm. Algebra 26(4), 1209–1231...
  • Maggioni R., Ragusa A.: The Hilbert function of generic plane sections of curves of P 3. Invent. Math. 91(2), 253–258 (1988)
  • Migliore, J.C.: Introduction to liaison theory and deficiency modules. Progress in Mathematics, vol. 165. Birkhäuser Boston Inc., Boston,...
  • Nagel, U.: On Hilbert function under liaison, Matematiche (Catania) 46(1991)(2), 547–558 (1993)
  • Nollet S.: Integral subschemes of codimension two. J. Pure Appl. Algebra 141(3), 269–288 (1999)
  • Orecchia, F., Cioffi, F., Ramella, I.: Points (software for computations on points). Available for linux platform at http://wpage.unina.it/cioffifr/EPoints.html...
  • Robbiano L.: An introduction to the theory of Hilbert functions. The Curves Seminar at Queen’s VII, B1–B26 (1990)
  • Evelina Rossi, M., Trung, N.V., Valla, G.: Castelnuovo–Mumford regularity and finiteness of Hilbert functions. Commutative algebra. Lect....
  • Valla, G.: Problems and results on Hilbert functions of graded algebras. Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math.,...