Journal of Differential Geometry

Lines on the Dwork quintic pencil and its higher degree analogues

Don Zagier

Full-text: Open access

Abstract

We give a reformulation of the recent results of Candelas et al., Lines on the Dwork pencil of quintic threefolds, describing pencils of lines on the quintic threefold $$ \{ (x_1 : \dots : x_5) \in \mathbb{P}^4 (\mathbb{C}) \ {} \vert \ {} x^5_1 + \dots + x^5_5 = 5{\psi}x_1 \dots x_5 \} $$ in terms of the moduli space $M_{0,5}$ of curves of genus $0$ with $5$ marked points, and a generalization to pencils of lines on the degree $n$ hypersurfaces $$ \{ (x_1 : \dots : x_n) \in \mathbb{P}^{n-1} (\mathbb{C}) \ {} \vert \ {} x^n_1 + \dots + x^n_n = n{\psi}x_1 \dots x_n \} $$ in $\mathbb{P}^{n−1}(\mathbb{C})$ in terms of the moduli space $M_{0,n}$ for any odd integer $n \geq 5$.

Article information

Source
J. Differential Geom., Volume 97, Number 1 (2014), 177-189.

Dates
First available in Project Euclid: 9 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1404912108

Digital Object Identifier
doi:10.4310/jdg/1404912108

Mathematical Reviews number (MathSciNet)
MR3229055

Zentralblatt MATH identifier
1328.14069

Citation

Zagier, Don. Lines on the Dwork quintic pencil and its higher degree analogues. J. Differential Geom. 97 (2014), no. 1, 177--189. doi:10.4310/jdg/1404912108. https://projecteuclid.org/euclid.jdg/1404912108


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