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Á¦¸ñ: Automorphisms of elliptic curves and K3 surfaces
ÃÊ·Ï: K3 surfaces are 2-dimensional analogues of elliptic curves.
Algebraic K3 surfaces form a 19 dimensional moduli space with infinitely many components,
while elliptic curves form a 1 dimensional moduli.
A general K3 surface does not admit an elliptic fibration structure,
so cannot be expresssed by a Weierstrass equation, while every elliptic curve can be.
This explains the huge difference between the study of K3 surfaces and elliptic curves.
K3 surfaces have been extensively studied by many authors,
and numerous important results are known such as periods and Torelli Theorem,
description of moduli spaces of K3 surfaces, computation of the automorphism groups of K3 surfaces,
and classification of finite groups which may act symplectically on a K3 surface, etc.
In this talk, I will focus on a yet another fundamental question:
what are the possible orders of automorphisms of K3 surfaces?
We give a precise answer to the question in all characterisitcs except 2 and 3.
Our result is comparable with the well known result on elliptic curves.