Gallarati studied contact of surfaces in $\mathbb{P}^3$, that is surfaces $V,W \subset \mathbb{P}^3$ such that $V.W = qD$ with $q$ an integer that is at least 2 and $D$ some curve.

I would like to read his results, contained in the 1960 paper "Ricerche sul contatto di superficie algebriche lungo curve". However, this is in Italian and uses older language of algebraic geometry.

Does anyone know a place where to find his results in more modern language, and in English? (French or German will also suffice.)

Edit: A more precise reference can be found at


or at (thanks Carlo Beenakker!)


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    $\begingroup$ Do you have a precise reference for this paper? $\endgroup$ Apr 25, 2013 at 3:43
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    $\begingroup$ it's in the proceedings of the Belgian Academy of Sciences, here is the bibliographic link, they'll send you a scan if you pay them a few Euro's: academieroyale.be/… $\endgroup$ Apr 25, 2013 at 6:35
  • $\begingroup$ @Filippo, i have added the mathscinet reference. Thanks, i should have done this straight away. $\endgroup$
    – Joachim
    Apr 25, 2013 at 13:32
  • $\begingroup$ @Carlo Thanks! If there is no modern reference i'll buy the paper there (and ask an Italian friend for help). $\endgroup$
    – Joachim
    Apr 25, 2013 at 13:33
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    $\begingroup$ Wow, it is 78 pages long... I swear I would have tried, but it seems to be a loooooong task ;-) $\endgroup$ Apr 25, 2013 at 17:29

1 Answer 1


I think Gallarati's construction is explained in modern terms in this paper: http://math.mit.edu/~ssam/papers/Catanese.pdf.

(Disclaimer: I've never looked at Gallarati's paper, so I'm not sure whether it has all been reworked in the above reference or not).

  • $\begingroup$ Thanks! I read Casnati's paper before, it's very interesting. However, i'm sure it does not contain all of Gallarati's results (for example there a big difference in the amount of pages). If no new answers pop up i'll accept yours, but i will wait a little bit before doing that. $\endgroup$
    – Joachim
    Apr 26, 2013 at 13:30
  • $\begingroup$ I hope you get a more complete answer. $\endgroup$
    – rita
    Apr 26, 2013 at 20:27
  • $\begingroup$ To anyone reading this in a later stage: from the people using Gallarati's results, at least Stephan Endrass and Fabrizio Catanese (i believe) read the original paper, and i suspect there is no modern version. Time for me to learn Italian. $\endgroup$
    – Joachim
    Apr 29, 2013 at 10:08

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