The Dimension of the Hilbert Scheme of Special ThreefoldsFootnote^#

^#Communicated by L. Ein.

REFERENCES

• Abo , H. , Decker , W. , Sasakura , N. ( 1997 ). An elliptic conic bundle in ℙ4 arising from a stable rank-3 vector bundle . Math. Z. 229 ( 4 ): 725 – 748 . [CSA]
   Web of Science ®Google Scholar
• Beltrametti , M. , Schneider , M. , Sommese , A. J. ( 1990 ). Threefolds of degree 9 and 10 in ℙ5 . Math. Ann. 288 ( 3 ): 413 – 444 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Beltrametti , M. , Schneider , M. , Sommese , A. J. ( 1992 ). Threefolds of degree 11 in ℙ5 . Complex Projective Geometry, Bergen – Trieste . Number 179 in London Math. Soc. Lecture Notes . Cambridge : Cambridge Univ. Press , pp. 59 – 80 .
   Google Scholar
• Beltrametti , M. , Sommese , A. J. ( 1995 ). The Adjunction Theory of Complex Projective Varieties . Vol. 16 of Expositions in Mathematics . Berlin : De Gruyter .
   Google Scholar
• Bertolini , M. ( 2004 ). Threefolds in ℙ6 of degree twelve . Preprint .
   Google Scholar
• Besana , G. M. , Biancofiore , A. ( 2005 ). Degree eleven manifolds of dimension greater or equal to three . Forum Mathematicum 17 ( 5 ): 711 – 733 . [CSA]
   Web of Science ®Google Scholar
• Biancofiore , A. , Fania , M. L. ( 2001 ). On the structure of linked threefolds . Rev. Mat. Complut. ( 1 ): 17 – 44 . [CSA]
   Google Scholar
• Braun , R. , Ottaviani , G. , Schneider , M. , Schreyer , F.-O. ( 1993 ). Boundedness for nongeneral-type 3-folds in ℙ5 . Complex Analysis and Geometry . Univ. Ser. Math . New York : Plenum , pp. 311 – 338 .
   Google Scholar
• Chang , M.-C. ( 1996 ). The number of components of Hilbert schemes . Internat. J. Math. 7 ( 3 ): 301 – 306 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Chang , M.-C. ( 1997 ). Inequidimensionality of Hilbert schemes . Proc. Amer. Math. Soc. 125 ( 9 ): 2521 – 2526 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• D'Souza , H. ( 1988 ). Threefolds whose hyperplane sections are elliptic surfaces . Pacific J. Math. 134 ( 1 ): 57 – 78 . [CSA]
   Web of Science ®Google Scholar
• Ellingsrud , G. ( 1975 ). Sur le schéma de Hilbert des variétés de codimension 2 dans ℙ e a cône de Cohen-Macaulay . Ann. scient. Éc. Norm. Sup. 4 ^e serie 8 ( 4 ): 423 – 432 . [CSA]
   Web of Science ®Google Scholar
• Fania , M. L. , Livorni , E. L. ( 1993 ). Polarized manifolds of dimension ≥3, Δ-genus three, dim Bs|L| ≤ 0 and degree ≥2 Δ − 1 . Saitama Math. Journal 11 : 41 – 58 . [CSA]
   Google Scholar
• Fania , M. L. , Livorni , E. L. (1994). Degree nine manifolds of dimension ≥3. Math. Nachr. 169:117–134. [CSA]
   Web of Science ®Google Scholar
• Fania , M. L. , Livorni , E. L. ( 1997 ). Degree ten manifolds of dimension n greater than or equal to 3 . Math. Nachr. 188 : 79 – 108 . [CSA]
   Web of Science ®Google Scholar
• Fania , M. L. , Mezzetti , E. ( 2002 ). On the Hilbert scheme of Palatini threefolds . Advances in Geometry 2 ( 4 ): 371 – 389 . [CSA]
   Web of Science ®Google Scholar
• Fujita , T. ( 1987 ). Classification of polarized manifolds of sectional genus two . Algebraic Geometry and Commutative Algebra in honor of Masayoshi Nagata . Tokyo : Kinokuniya , pp. 73 – 98 .
   Google Scholar
• Grothendieck , A. ( 1960 ). Techniques de construction et théorèmes d'existence en géométrie algébrique. IV: les schémas de Hilbert . Number 221 in Seminaire Bourbaki .
   Google Scholar
• Hartshorne , R. ( 1977 ). Algebraic Geometry . Number 52 in Graduate Text in Math . New York-Heidelberg-Berlin : Springer Verlag .
   Google Scholar
• Ionescu , P. ( 1984 ). Embedded projective varieties of small invariants . In: Proceedings of the Week of Algebraic Geometry Bucharest 1982 . Number 1056 in Lecture Notes in Mathematics . Springer Verlag , pp. 142 – 186 .
   Google Scholar
• Ionescu , P. ( 1986 ). Generalized adjunction and applications . Math. Proc. Camb. Phil. Soc. 99 : 457 – 472 . [CSA]
   Web of Science ®Google Scholar
• Ionescu , P. ( 1990 ). Embedded projective varieties of small invariants III . Algebraic Geometry L'Aquila 1988 . Number 1417 in Lecture Notes in Mathematics . Berlin : Springer Verlag , pp. 138 – 154 .
   Google Scholar
• Kleppe , J. O. , Migliore , J. C. , Miró-Roig , R. , Nagel , U. , Peterson , C. ( 2001 ). Gorenstein liaison, complete intersection liaison invariants and unobstructedness . Mem. Amer. Math. Soc. 154 ( 732 ): viii+116 . [CSA]
   Web of Science ®Google Scholar
• Kleppe , J. O. , Miró-Roig , R. M. ( 1998 ). The dimension of the Hilbert scheme of Gorenstein codimension 3 subschemes . J. Pure Appl. Algebra 127 : 73 – 82 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Okonek , C. ( 1984 ). Über 2-codimensionale Untermannigfaltigkeiten vom Grad 7 im ℙ4 und ℙ5 . Math. Z. 187 ( 2 ): 209 – 219 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Okonek , C. ( 1986 ). Flächen vom Grad 8 im P 4 . Math. Z. 191 ( 2 ): 207 – 223 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• Okonek , C. ( 1994 ). Notes on varieties of codimension 3 in P n . Manuscripta Math. 84 : 421 – 442 . [CSA]
   Web of Science ®Google Scholar
• Okonek , C. , Schneider , M. , Spindler , H. ( 1980 ). Vector Bundles on Complex Projective Spaces . Number 3 in Progress in Mathematics . Boston-Basel-Stuttgart : Birkhäuser .
   Google Scholar
• Ottaviani , G. ( 1992 ). On 3-folds in ℙ5 which are scrolls . Annali della Scuola Normale di Pisa Scienze Fisiche e Matematiche IV-XIX ( 3 ): 451 – 471 . [CSA]
   Google Scholar
• Sommese , A. J. ( 1981 ). On the minimality of hyperplane sections of projective threefolds . J. Reine Angew. Math. 329 : 16 – 41 . [CSA]
   Web of Science ®Google Scholar
• Swinnerton Dyer , H. ( 1973 ). An enumeration of all varieties of degree 4 . American Journal of Math 95 : 403 – 418 . [CSA]
   Web of Science ®Google Scholar
• Weil . ( 1957 ). American Journal of Mathematics . 79 : 951 – 952 . Now in A. Weil, Oeuvres Sc. II , 555 – 556 . [CSA]
   Google Scholar
• # Communicated by L. Ein.
   Google Scholar