Counting lines and conics on a surface
type: Item
instance of: scholarly article
title: Counting lines and conics on a surface
zbMATH Open document ID: 1185.14050
author: Yoichi Miyaoka
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2009-11-04T00:00:00Z
review text: The problem of studying the number of lines on surfaces in \(\mathbb{P}^3_{\mathbb{C}}\) is classical and it was started by \textit{B. Segre} [Q. J. Math., Oxf. Ser. 14, 86--96 (1943; Zbl 0063.06860); Proc. Lond. Math. Soc. (2) 49, 353--395 (1947; Zbl 0034.08603)]. Then many authors improved the bounds for the maximal number of lines on a surface in \(\mathbb{P}^3_{\mathbb{C}}\). The author study the problem from a more general point of view and he gives bounds for the number of rational curves and elliptic curves on complex pojective algebraic surfaces and he produce example of surfaces satisfying the upper bounds.
reviewed by: Alessandra Sarti
Mathematics Subject Classification ID: 14N15
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14J29
zbMATH DE Number: 5625043
zbMATH Keywords: projective surfaces
zbMATH Keywords: rational curves
zbMATH Keywords: elliptic curves
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1249478969
OpenAlex ID: W592250703
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DOI: 10.2977/PRIMS/1249478969
description: scientific article; zbMATH DE number 5625043