A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$

Ronconi, M. Cristina

A Regular Threefold of General Type with

p_{g}=0

and

P_{2}=6

Ronconi, M. Cristina

Bollettino dell'Unione Matematica Italiana, Tome 2 (2009), p. 607-621 / Harvested from Biblioteca Digitale Italiana di Matematica

Access to full text
Full (PDF)
Full (DjVu)

Résumé

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 $P_{2}\leq 5$ . 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.

Publié le : 2009-10-01

MR 2569294 | Zbl 1184.14069

@article{BUMI_2009_9_2_3_607_0,
     author = {M. Cristina Ronconi},
     title = {A Regular Threefold of General Type with $p\_{g} = 0$ and $P\_{2} = 6$},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2},
     year = {2009},
     pages = {607-621},
     zbl = {1184.14069},
     mrnumber = {2569294},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2009_9_2_3_607_0}
}

Ronconi, M. Cristina. A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$. Bollettino dell'Unione Matematica Italiana, Tome 2 (2009) pp. 607-621. http://gdmltest.u-ga.fr/item/BUMI_2009_9_2_3_607_0/

Bibliographie

[1] Gattazzo, R., Examples of threefolds with $q_{1}=q_{2}=p_{g}=0$ and $3\leq P_{2}\leq 4$ , preprint. | MR 2799358 | Zbl 1218.14008

[2] Griffiths, Ph. - Harris, J., Principles of Algebraic Geometry, Wiley (New York, 1978). | MR 507725 | Zbl 0408.14001

[3] Iano-Fletcher, A. R., 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] Iitaka, S., Algebraic Geometry (Springer-Verlag, New York-Berlin, 1982). | MR 637060

[5] Reid, M., 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

[6] Ronconi, M. C., A Threefold of general type with $q_{1}=q_{2}=p_{g}=P_{2}=0$ , Acta Appl. Math., 75, no. 1-3 (2003), 133-150. | MR 1975564 | Zbl 1051.14047

[7] Stagnaro, E., 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

[8] Stagnaro, E., Adjoints and pluricanonical adjoints to an algebraic hypersurface, Ann. Mat. Pura Appl., (4), 180, no. 2 (2001), 147-201. | MR 1847403 | Zbl 1072.14044

[9] Stagnaro, E., Gaps in the birationality of pluricanonical transformations, Accademia Ligure di Sc. e Lettere, Collana di Studi e Ricerche (Genova, 2004), 5-53.

[10] Stagnaro, E., A threefold with $p_{g}=0$ and $P_{2}=2$ , Rend. Semin. Mat. Univ. Padova, 121 (2009), 13-31. | MR 2542132