Ronconi, M. Cristina:
A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$
Bollettino dell'Unione Matematica Italiana Serie 9 2 (2009), fasc. n.3, p. 607-621, (English)
pdf (200 Kb), djvu (158 Kb). | MR 2569294 | Zbl 1184.14069
Sunto
The range of the bigenus $P_{2}$ is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with $p_{g} = 0$: The examples in the literature have $P_{2} \le 5$. In the present paper we present a non-singular threefold with $p_{g} = q_{1} = q_{2} = 0$; $P_{2} = 6$; the bicanonical map is stably birational.
Referenze Bibliografiche
[1]
R. GATTAZZO,
Examples of threefolds with $q_{1} = q_{2} = p_{g} = 0$ and $3 \le P_{2} \le 4$, preprint. |
MR 2799358 |
Zbl 1218.14008[2]
PH. GRIFFITHS -
J. HARRIS,
Principles of Algebraic Geometry,
Wiley (New York,
1978). |
MR 507725 |
Zbl 0408.14001[3]
A. R. IANO-FLETCHER,
Working with weighted complete intersections,
Explicit birational Geometry of 3-folds,
London Math. Soc., Lecture Note Ser. 281,
Cambridge Univ. Press (Cambridge,
2000), 101-173. |
MR 1798982 |
Zbl 0960.14027[4]
S. IITAKA,
Algebraic Geometry (
Springer-Verlag, New York-Berlin,
1982). |
MR 637060[5]
M. REID,
Young person's guide to canonical singularities,
Algebraic Geometry, Bowdoin, 1985,
Proc. Sympos. Pure Math.,
46, Part 1,
Amer. Math. Soc., Providence (
1987), 345-414. |
MR 927963[7]
E. STAGNARO,
Pluricanonical maps of a threefold of general type,
Proc. of Greco Conference on Commutative Algebra and Algebraic Geometry, (Catania, 2001).
Le Matematiche (Catania),
55, no. 2 (
2000) (
2002), 533-543. |
MR 1984218 |
Zbl 1072.14045[9] E. STAGNARO, Gaps in the birationality of pluricanonical transformations, Accademia Ligure di Sc. e Lettere, Collana di Studi e Ricerche (Genova, 2004), 5-53.
Con il contributo del Ministero per i Beni e le AttivitĂ Culturali