Certain Minimal Varieties Are Set-Theoretic Complete Intersections

REFERENCES

• Barile , M. ( 1995 ). Arithmetical ranks of ideals associated to symmetric and alternating matrices . J. Algebra 176 : 59 – 82 .
   Web of Science ®Google Scholar
• Barile , M. ( 1996 ). On the number of equations defining certain varieties . Manuscripta Math. 91 : 483 – 494 .
   Web of Science ®Google Scholar
• Barile , M. (2004). On the computation of arithmetical ranks. Int. J. Pure Appl. Math. 17:143–161.
   Google Scholar
• Barile , M. , Morales , M. ( 1998 ). On certain algebras of reduction number one . J. Algebra 206 : 113 – 128 .
   Google Scholar
• Barile , M. , Morales , M. ( 2000 ). On the equations defining minimal varieties . Comm. Algebra 28 : 1223 – 1239 .
   Web of Science ®Google Scholar
• Barile , M. , Morales , M. ( 2004 ). On unions of scrolls along linear spaces . Rend. Sem. Mat. Univ. Padova 111 : 161 – 178 .
   Google Scholar
• Barile , M. , Lyubeznik , G. ( 2005 ). Set-theoretic complete intersections in characteristic p . Proc. Amer. Math. Soc. 133 : 3199 – 3209 .
   Google Scholar
• Barile , M. , Morales , M. , Thoma , A. ( 2002 ). Set-theoretic complete intersections on binomials . Proc. Amer. Math. Soc. 130 : 1893 – 1903 .
   Google Scholar
• Bresinsky , H. ( 1979 ). Monomial Gorenstein curves in A 4 are set-theoretic complete intersections . Manuscripta Math. 27 : 353 – 358 .
   Google Scholar
• Bruns , W. , Schwänzl , R. ( 1990 ). The number of equations defining a determinantal variety . Bull. London Math. Soc. 22 : 439 – 445 .
   Web of Science ®Google Scholar
• CoCoATeam . ( 2005 ). CoCoA, a system for doing computations in commutative algebra . Available at http://cocoa.dima.unige.it
   Google Scholar
• Eisenbud , D. , Goto , S. ( 1984 ). Linear free resolutions and minimal multiplicity . J. Algebra 88 : 89 – 133 .
   Web of Science ®Google Scholar
• Eliahou , S. ( 1984 ). Idéaux de définition des courbes monomiales . In: Greco , S. , Strano , R. , eds. Complete Intersections . Lecture Notes in Mathematics 1092 . Springer , pp. 229 – 240 .
   Google Scholar
• Eto , K. ( 1994 ). Almost complete intersection monomial curves in A 4 . Comm. Algebra 22 : 5325 – 5342 .
   Web of Science ®Google Scholar
• Giménez , Ph. ( 1993 ). Étude de la Fibre Spéciale de L'éclatement D'une Variété Monomiale en Codimension Deux. Dissertation. Institut Fourier, Université de Grenoble I .
   Google Scholar
• Giménez , Ph. , Morales , M. , Simis , A. ( 1994 ). L'analytic spread de l'idéal de définition d'une variété monomiale de codimension deux est toujours inférieur ou égal à trois. (The analytic spread of the ideal of definition of a codimension 2 monomial variety is always less or equal to 3) . C. R. Acad. Sci., Paris, Sér. I 319 : 703 – 706 .
   Google Scholar
• Harris , J. ( 1992 ). Algebraic Geometry . Springer .
   Google Scholar
• Huneke , C. ( 2004 ). Lectures on local cohomology (Appendix 1 by Amelia Taylor). Available at http://www.math.uic.edu/~bshipley/huneke.pdf
   Google Scholar
• Katsabekis , A. ( 2005 ). Projection of cones and the arithmetical rank of toric varieties . J. Pure Appl. Algebra 199 : 133 – 147 .
   Google Scholar
• Lyubeznik , G. ( 1984 ). On the local cohomology modules for ideals  generated by monomials in an R-sequence . In: Greco , S. , Strano , R. , eds. Complete Intersections . Lect. Notes Math. 1092 . Springer , pp. e 214 – 220 .
   Google Scholar
• Milne , J. S. ( 1998 ). Lectures on étale cohomology. Available at http://www.jmilne.org
   Google Scholar
• Newstead , P. E. ( 1980 ). Some subvarieties of Grassmannians of codimension 3 . Bull. London Math. Soc. 12 : 176 – 182 .
   Google Scholar
• Patil , D. P. ( 1990 ). Certain monomial curves are set-theoretic complete intersections . Manuscripta Math. 68 : 399 – 404 .
   Web of Science ®Google Scholar
• Peskine , C. , Szpiro , L. ( 1973 ). Dimension finie et cohomologie locale . Publ. Math. IHES 42 : 47 – 119 .
   Google Scholar
• Robbiano , L. , Valla , G. ( 1983a ). Some curves in P 3 are set-theoretic complete intersections . In: Ciliberto , C. , Ghione , F. , Orecchia , F. , eds. Algebraic Geometry-Open Problems . Lect. Notes Math. 997 . Springer , pp. 391 – 399 .
   Google Scholar
• Robbiano , L. , Valla , G. ( 1983b ). On set-theoretic complete intersections in the projective space . Rend. Semin. Mat. Fis. Milano LIII : 333 – 346 .
   Google Scholar
• Schmitt , Th. , Vogel , W. (1979). Note on set-theoretic intersections of subvarieties of projective space. Math. Ann. 245:247–253.
   Web of Science ®Google Scholar
• Verdi , L. ( 1979 ). Le curve razionali normali come intersezioni complete insiemistiche . Boll. UMI 16-A : 385 – 390 .
   Google Scholar
• Xambó , S. ( 1981 ). On projective varieties of minimal degree . Collect. Math. 32 : 149 – 163 .
   Google Scholar
• Yan , Z. ( 2000 ). An étale analog of the Goresky-MacPherson formula for subspace arrangements . J. Pure Appl. Algebra 146 : 305 – 318 .
   Web of Science ®Google Scholar
• Communicated by R. H. Villarreal.
   Google Scholar