1,925 research outputs found
K3 surfaces with a non-symplectic automorphism and product-quotient surfaces with cyclic groups
We classify all the K3 surfaces which are minimal models of the quotient of
the product of two curves by the diagonal action of either the
group or the group . These K3 surfaces admit a non-symplectic
automorphism of order induced by an automorphism of one of the curves
or . We prove that most of the K3 surfaces admitting a non-symplectic
automorphism of order (and in fact a maximal irreducible component of the
moduli space of K3 surfaces with a non-symplectic automorphism of order )
are obtained in this way.\\ In addition, we show that one can obtain the same
set of K3 surfaces under more restrictive assumptions namely one of the two
curves, say , is isomorphic to a rigid hyperelliptic curve with an
automorphism of order and the automorphism of the K3 surface is
induced by .\\ Finally, we describe the variation of the Hodge
structures of the surfaces constructed and we give an equation for some of
them.Comment: 30 pages, 2 figure
Random enriched trees with applications to random graphs
We establish limit theorems that describe the asymptotic local and global
geometric behaviour of random enriched trees considered up to symmetry. We
apply these general results to random unlabelled weighted rooted graphs and
uniform random unlabelled -trees that are rooted at a -clique of
distinguishable vertices. For both models we establish a Gromov--Hausdorff
scaling limit, a Benjamini--Schramm limit, and a local weak limit that
describes the asymptotic shape near the fixed root
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