Journal of Mathematics of Kyoto University

Minimal algebraic surfaces of general type with $c^2_1 = 3, p_g = 1 \text{ and } q = 0$, which have non-trivial 3-torsion divisors

Masaaki Murakami

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Abstract

We shall give a concrete description of minimal algebraic surfaces $X$’s defined over $\mathbb{C}$ of general type with the first chern number 3, the geometric genus 1 and the irregularity 0, which have non-trivial 3-torsion divisors. Namely, we shall show that the fundamental group is isomorphic to $\mathbb{Z}/3$, and that the canonical model of the universal cover is a complete intersection in $\mathbb{P}^{4}$ of type (3, 3).

Article information

Source
J. Math. Kyoto Univ., Volume 43, Number 1 (2003), 203-215.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250283747

Digital Object Identifier
doi:10.1215/kjm/1250283747

Mathematical Reviews number (MathSciNet)
MR2028707

Zentralblatt MATH identifier
1061.14035

Subjects
Primary: 14J29: Surfaces of general type
Secondary: 14E20: Coverings [See also 14H30] 14J10: Families, moduli, classification: algebraic theory

Citation

Murakami, Masaaki. Minimal algebraic surfaces of general type with $c^2_1 = 3, p_g = 1 \text{ and } q = 0$, which have non-trivial 3-torsion divisors. J. Math. Kyoto Univ. 43 (2003), no. 1, 203--215. doi:10.1215/kjm/1250283747. https://projecteuclid.org/euclid.kjm/1250283747


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