## Journal of Differential Geometry

### Lines on the Dwork quintic pencil and its higher degree analogues

Don Zagier

#### 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