TY - JOUR
AU - Auffarth, Robert
AU - Lucchini Arteche, Giancarlo
AU - Quezada, Pablo
PY - 2022/04/04
Y2 - 2024/02/21
TI - Smooth quotients of abelian surfaces by finite groups that fix the origin
JF - CUBO, A Mathematical Journal
JA - CUBO
VL - 24
IS - 1
SE - Articles
DO - 10.4067/S0719-06462022000100037
UR - https://cubo.ufro.cl/ojs/index.php/cubo/article/view/2953
SP - 37–51
AB - <p class="p1">Let \(A\) be an abelian surface and let \(G\) be a finite group of automorphisms of \(A\) fixing the origin. Assume that the analytic representation of \(G\) is irreducible. We give a classification of the pairs \((A,G)\) such that the quotient \(A/G\) is smooth. In particular, we prove that \(A=E^2\) with \(E\) an elliptic curve and that \(A/G\simeq\mathbb P^2\) in all cases. Moreover, for fixed \(E\), there are only finitely many pairs \((E^2,G)\) up to isomorphism. This fills a small gap in the literature and completes the classification of smooth quotients of abelian varieties by finite groups fixing the origin started by the first two authors.</p>
ER -