edoc: No conditions. Results ordered -Date Deposited. 2024-09-13T15:53:21ZEPrintshttps://edoc.unibas.ch/images/uni-logo.jpghttps://edoc.unibas.ch/2018-04-04T07:13:23Z2018-04-04T07:13:23Zhttps://edoc.unibas.ch/id/eprint/39402This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/394022018-04-04T07:13:23ZThe group of Cremona transformations generated by linear maps and the standard involutionThis article studies the group generated by automorphisms of the projective space of dimension n and by the standard birational involution of degree n . Every element of this group only contracts rational hypersurfaces, but in odd dimension, there are simple elements having this property which do not belong to the group. Geometric properties of the elements of the group are given, as well as a description of its intersection with monomial transformations. Jérémy BlancIsac Hedén2017-08-21T12:43:19Z2022-02-08T18:11:46Zhttps://edoc.unibas.ch/id/eprint/42537This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/425372017-08-21T12:43:19ZThe decomposition group of a line in the planeWe show that the decomposition group of a line L in the plane, i.e. the subgroup of plane birational transformations that send L to itself birationally, is generated by its elements of degree 1 and one element of degree 2, and that it does not decompose as a non-trivial amalgamated product. Isac HedénSusanna Zimmermann2016-11-29T10:26:50Z2016-11-29T10:26:50Zhttps://edoc.unibas.ch/id/eprint/42980This item is in the repository with the URL: https://edoc.unibas.ch/id/eprint/429802016-11-29T10:26:50ZAffine Extensions of Principal Additive Bundles over a Punctured SurfaceThe aim of this article is to make a first step towards the classification of complex normal affine $G_a$-threefolds $X$. We consider the case where the restriction of the quotient morphism $picolon Xto S$ to $pi^{-1}(S_*)$, where $S_*$ denotes the complement of some regular closed point in $S$, is a principal $G_a$-bundle. The variety $SL_2$ will be of special interest and a source of many examples. It has a natural right $G_a$-action such that the quotient morphism $SL_2toA^2$ restricts to a principal $G_a$-bundle over the punctured plane $A^2_*$. Isac Hedén