Advanced Studies in Pure Mathematics

On the Castelnuovo-Weil lattices, I

Viet Nguyen-Khac and Tetsuji Shioda

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Abstract

The Castelnuovo-Weil lattice of a curve refers to the ring of correspondence of the curve or the endomorphism ring of its Jacobian variety, viewed as a lattice with respect to the natural trace form. The main subject is the minimal norm $\mu (C)$ of this lattice, and we discuss the question as to whether $\mu (C) = 2g$ holds true.

Article information

Source
Algebraic Geometry in East Asia — Hanoi 2005, K. Konno and V. Nguyen-Khac, eds. (Tokyo: Mathematical Society of Japan, 2008), 333-344

Dates
Received: 19 September 2006
Revised: 9 May 2007
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1545001313

Digital Object Identifier
doi:10.2969/aspm/05010333

Mathematical Reviews number (MathSciNet)
MR2409564

Zentralblatt MATH identifier
1151.11327

Subjects
Primary: 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25] 11G10: Abelian varieties of dimension > 1 [See also 14Kxx] 14H31

Citation

Nguyen-Khac, Viet; Shioda, Tetsuji. On the Castelnuovo-Weil lattices, I. Algebraic Geometry in East Asia — Hanoi 2005, 333--344, Mathematical Society of Japan, Tokyo, Japan, 2008. doi:10.2969/aspm/05010333. https://projecteuclid.org/euclid.aspm/1545001313


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