[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j200534

THE MAIN COMPONENT OF A REDUCIBLE HILBERT CURVE OF CONIC FIBRATIONS

Fania, Maria Lucia (DISIM, Universita degli Studi dell'Aquila)
Lanteri, Antonio (Dipartimento di Matematica "F. Enriques" Universita degli Studi di Milano)

Publication Information

Journal of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1211-1226 More about this Journal

Abstract

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

Keywords

Conic fibration; scroll; Hilbert curve;

Citations & Related Records

Reference

1	W. P. Barth, K. Hulek, C. A. M. Peters, and A. Van de Ven, Compact complex surfaces, second edition, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 4, Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/978-3-642-57739-0
2	M. Beltrametti, A. Lanteri, and M. Palleschi, Algebraic surfaces containing an ample divisor of arithmetic genus two, Ark. Mat. 25 (1987), no. 2, 189-210. https://doi.org/10.1007/BF02384443 DOI
3	M. C. Beltrametti, A. Lanteri, and A. J. Sommese, Hilbert curves of polarized varieties, J. Pure Appl. Algebra 214 (2010), no. 4, 461-479. https://doi.org/10.1016/j.jpaa.2009.06.009 DOI
4	F. A. Bogomolov, Holomorphic tensors and vector bundles on projective manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), no. 6, 1227-1287, 1439.
5	M. L. Fania and A. Lanteri, Hilbert curves of conic fibrations over smooth surfaces, Comm. Algebra 49 (2021), no. 2, 545-566. https://doi.org/10.1080/00927872.2020.1807022 DOI
6	T. Fujita, Classification theories of polarized varieties, London Mathematical Society Lecture Note Series, 155, Cambridge University Press, Cambridge, 1990. https://doi.org/10.1017/CBO9780511662638
7	R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York, 1977.
8	A. Lanteri, Characterizing scrolls via the Hilbert curve, Internat. J. Math. 25 (2014), no. 11, 1450101, 17 pp. https://doi.org/10.1142/S0129167X14501018 DOI
9	A. Lanteri, Hilbert curves of 3-dimensional scrolls over surfaces, J. Pure Appl. Algebra 222 (2018), no. 1, 139-154. https://doi.org/10.1016/j.jpaa.2017.03.008 DOI
10	H. Maeda, On polarized surfaces of sectional genus three, Sci. Papers College Arts Sci. Univ. Tokyo 37 (1988), no. 2, 103-112.
11	K. Yokoyama, On blowing-up of polarized surfaces, J. Math. Soc. Japan 51 (1999), no. 3, 523-533. https://doi.org/10.2969/jmsj/05130523 DOI
12	A. Lanteri and A. L. Tironi, Hilbert curve characterizations of some relevant polarized manifolds, arXiv: 1803.01131, 2018.