SCROLLS AND HYPERBOLICITY-Reference-Cited by-同舟云学术

SCROLLS AND HYPERBOLICITY

Published:2013-04 Issue:04 Volume:24 Page:1350026
ISSN:0129-167X
Container-title:International Journal of Mathematics
language:en
Short-container-title:Int. J. Math.

Author:

CILIBERTO C.¹,ZAIDENBERG M.²

Affiliation:

1. Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy

2. Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, BP 74, 38402 Saint Martin d'Hères Cédex, France

Abstract

Using degeneration to scrolls, we give an easy proof of non-existence of curves of low genera on general surfaces in ℙ3of degree d ≥ 5. We also show that there exist Kobayashi hyperbolic surfaces in ℙ3of degree d = 7 (a result so far unknown), and give a new construction of such surfaces of degree d = 6. Our method yields also some lower bounds for geometric genera of surfaces lying on general hypersurfaces of degree 3d ≥ 15 in ℙ4.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129167X13500262

Reference53 articles.

1. Sulle condizioni perchè una curva algebrica riducibile si opssa considerare come limite di una curva algebrica irriducibile

2. Footnotes to a paper of Beniamino Segre

3. On regular and stable ruled surfaces in P3

4. Lectures on Curves, Surfaces and Projective Varieties

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