6
$\begingroup$

I have listened to lectures that mention Jonquières automorphisms for affine spaces by name. They don't seem to be found in textbooks on algebraic geometry. I would like to know the exact reference preferably for the original work where it can be found.

I have access to Hanspeter Kraft's Bourbaki seminar talk Challenging Problems in Affine Spaces (1994-95, exp. 802). The bibliography there has more than hundred entries but not this.

I would be grateful to anyone who can point out the references.

Improve this question
$\endgroup$
4
  • 4
    $\begingroup$ E. de Jonquières: De la transformation géométrique des figures planes, et d'un mode de génération de certaines courbes à double courbure de tous les ordres. Nouv. Ann. (2) 3, 97--111 (1864). You can find it in Numdam. $\endgroup$
    – F Zaldivar
    Commented Dec 22, 2016 at 0:31
  • $\begingroup$ That was quick. I thought it might be before 1950, did not expect it to be from 19th century. Thank you very much. $\endgroup$
    – P Vanchinathan
    Commented Dec 22, 2016 at 0:37
  • $\begingroup$ @FZaldivar Why don't you promote this comment as an answer? $\endgroup$
    – Leo Alonso
    Commented Dec 22, 2016 at 10:50
  • $\begingroup$ @P Vanchinathan, you are welcome; @Leo Alonso, Ok. $\endgroup$
    – F Zaldivar
    Commented Dec 22, 2016 at 17:33

1 Answer 1

Reset to default
7
$\begingroup$

E. de Jonquières: De la transformation géométrique des figures planes, et d'un mode de génération de certaines courbes à double courbure de tous les ordres. Nouv. Ann. (2) 3, 97--111 (1864). You can find it in Numdam.

Improve this answer
$\endgroup$
4
  • 1
    $\begingroup$ I downloaded from Numdam and gave a cursory reading. My French is just enough for reading mathematics papers, but I could not exactly see where the automorphisms are defined. Is it too much of a bother if I ask you which section/page this is defined in that paper? (I have already submitted a paper in arxiv after including the above reference!) $\endgroup$
    – P Vanchinathan
    Commented Dec 22, 2016 at 23:42
  • 1
    $\begingroup$ In the paper, the description of the de Jonquières transformation, of order $n$, that sends a general line to a curve of order $n$, is given considering the net of curves of order $n$ with a common point of order $n-1$ and $2(n-1)$ common simple points, and a pencil of lines through the singular point. There are several places in the paper, starting in page 98 \S 2 to page 99 \S 4 where the de Jonquières transformation is described. Again, this is done in \S 6 and \S 7, pages 101--102 or in pages 104--105. $\endgroup$
    – F Zaldivar
    Commented Dec 23, 2016 at 3:39
  • 1
    $\begingroup$ ... Perhaps it is important to point out that this paper is a summary (see page 98 of the paper) of a longer article of de Jonquières, {\it M\'emoire sur les figures isographiques}, Giornale di Mathematische 23 (1885), 48--75. For a modern point of view, perhaps you may take a look at Chapter 7 of Dolgachev's \emph{Classical Algebraic Geometry: A Modern View}, CUP, 2012, especially Sections 7.2.3 and 7.3.6. One version of the book is available from the website of I. Dolgachev. $\endgroup$
    – F Zaldivar
    Commented Dec 23, 2016 at 3:39
  • $\begingroup$ ... order = degree $\endgroup$
    – F Zaldivar
    Commented Dec 23, 2016 at 3:49

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .