Translator Disclaimer
February 2018 Elliptic surfaces and contact conics for a 3-nodal quartic
Khulan TUMENBAYAR, Hiro-o TOKUNAGA
Hokkaido Math. J. 47(1): 223-244 (February 2018). DOI: 10.14492/hokmj/1520928068

Abstract

Let ${\mathcal Q}$ be an irreducible $3$-nodal quartic and let ${\mathcal C}$ be a smooth conic such that ${\mathcal C} \cap {\mathcal Q}$ does not contain any node of ${\mathcal Q}$ and the intersection multiplicity at $z \in {\mathcal C} \cap {\mathcal Q}$ is even for each $z$. In this paper, we study geometry of ${\mathcal C} + {\mathcal Q}$ through that of integral sections of a rational elliptic surface which canonically arises from ${\mathcal Q}$ and $z \in {\mathcal C} \cap {\mathcal Q}$. As an application, we construct Zariski pairs $({\mathcal C}_1 + {\mathcal Q}, {\mathcal C}_2 + {\mathcal Q})$, where ${\mathcal C}_i$ $(i = 1, 2)$ are smooth conics tangent to ${\mathcal Q}$ at four distinct points.

Citation

Download Citation

Khulan TUMENBAYAR. Hiro-o TOKUNAGA. "Elliptic surfaces and contact conics for a 3-nodal quartic." Hokkaido Math. J. 47 (1) 223 - 244, February 2018. https://doi.org/10.14492/hokmj/1520928068

Information

Published: February 2018
First available in Project Euclid: 13 March 2018

zbMATH: 06853599
MathSciNet: MR3773733
Digital Object Identifier: 10.14492/hokmj/1520928068

Subjects:
Primary: 14H30, 14H50, 14J27

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
22 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 1 • February 2018
Back to Top