Search results for "Automorphisms"
showing 4 items of 24 documents
Affine Surfaces With a Huge Group of Automorphisms
2013
We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.
Automorphisms of hyperelliptic GAG-codes
2009
Abstract We determine the n –automorphism group of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such group is, up to isomorphism, a subgroup of the automorphism group of the underlying function field.
Embedding mapping class groups of orientable surfaces with one boundary component
2012
We denote by $S_{g,b,p}$ an orientable surface of genus $g$ with $b$ boundary components and $p$ punctures. We construct homomorphisms from the mapping class groups of $S_{g,1,p}$ to the mapping class groups of $S_{g',1,(b-1)}$, where $b\geq 1$. These homomorphisms are constructed from branched or unbranched covers of $S_{g,1,0}$ with some properties. Our main result is that these homomorphisms are injective. For unbranched covers, this construction was introduced by McCarthy and Ivanov~\cite{IM}. They proved that the homomorphisms are injective. A particular cases of our embeddings is a theorem of Birman and Hilden that embeds the braid group on $p$ strands into the mapping class group of …
Automorphisms of Hyperelliptic GAG-codes
2008
In this talk, we discuss the n-automorphism groups of generalized algebraic-geometry codes associated with rational, elliptic and hyperelliptic function fields. Such groups are, up to isomorphism, subgroups of the automorphism groups of the underlying function fields. We also present some examples in which the n-automorphism groups can be determined explicitly.