Bollettino dell'Unione Matematica Italiana

, Volume 11, Issue 1, pp 13–25 | Cite as

Irrationality issues for projective surfaces

  • Francesco Bastianelli


This survey retraces the author’s talk at the Workshop Birational geometry of surfaces, Rome, January 11–15, 2016. We consider various birational invariants extending the notion of gonality to projective varieties of arbitrary dimension, and measuring the failure of a given projective variety to satisfy certain rationality properties, such as being uniruled, rationally connected, unirational, stably rational or rational. Then we review a series of results describing these invariants for various classes of projective surfaces.



I would like to thank the Organizers of the Workshop Birational geometry of surfaces and Andrea Bruno for encouraging me to think about this topic in view of the Workshop. I am grateful to Gian Pietro Pirola for introducing me to these problems when I was a Ph.D. student. I would also like to thank Andreas Knutsen for valuable suggestions.


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© Unione Matematica Italiana 2017

Authors and Affiliations

  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly

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