A Regular Threefold of General Type with p g = 0 and P 2 = 6

M. Cristina Ronconi

Bollettino dell'Unione Matematica Italiana (2009)

  • Volume: 2, Issue: 3, page 607-621
  • ISSN: 0392-4041

Abstract

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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 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.

How to cite

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Ronconi, M. Cristina. "A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$." Bollettino dell'Unione Matematica Italiana 2.3 (2009): 607-621. <http://eudml.org/doc/290581>.

@article{Ronconi2009,
abstract = {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.},
author = {Ronconi, M. Cristina},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {607-621},
publisher = {Unione Matematica Italiana},
title = {A Regular Threefold of General Type with $p_\{g\} = 0$ and $P_\{2\} = 6$},
url = {http://eudml.org/doc/290581},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Ronconi, M. Cristina
TI - A Regular Threefold of General Type with $p_{g} = 0$ and $P_{2} = 6$
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/10//
PB - Unione Matematica Italiana
VL - 2
IS - 3
SP - 607
EP - 621
AB - 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.
LA - eng
UR - http://eudml.org/doc/290581
ER -

References

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  1. GATTAZZO, R., Examples of threefolds with q 1 = q 2 = p g = 0 and 3 P 2 4 , preprint. Zbl1218.14008MR2799358
  2. GRIFFITHS, PH. - HARRIS, J., Principles of Algebraic Geometry, Wiley (New York, 1978). Zbl0408.14001MR507725
  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. Zbl0960.14027MR1798982
  4. IITAKA, S., Algebraic Geometry (Springer-Verlag, New York-Berlin, 1982). MR637060
  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. MR927963
  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. Zbl1051.14047MR1975564DOI10.1023/A:1022336011727
  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. Zbl1072.14045MR1984218
  8. STAGNARO, E., Adjoints and pluricanonical adjoints to an algebraic hypersurface, Ann. Mat. Pura Appl., (4), 180, no. 2 (2001), 147-201. Zbl1072.14044MR1847403DOI10.1007/s10231-001-8201-6
  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. MR2542132DOI10.4171/RSMUP/121-2

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