Bollettino dell'Unione Matematica Italiana

, Volume 11, Issue 1, pp 107–119 | Cite as

Monodromy representations and surfaces with maximal Albanese dimension

Article

Abstract

We relate the existence of some surfaces of general type and maximal Albanese dimension to the existence of some monodromy representations of the braid group \(\mathsf {B}_2(C_2)\) in the symmetric group \(\mathsf {S}_n\). Furthermore, we compute the number of such representations up to \(n=9\), and we analyze the cases \(n \in \{2, \, 3, \, 4\}\). For \(n=2, \, 3\) we recover some surfaces with \(p_g=q=2\) recently studied (with different methods) by the author and his collaborators, whereas for \(n=4\) we obtain some conjecturally new examples.

Keywords

Braid group Monodromy representation Surface of general type 

Mathematics Subject Classification

14J29 20F36 

Notes

Acknowledgements

The author was partially supported by GNSAGA-INdAM. He thanks the organizers of the workshop Birational Geometry of Surfaces (University of Rome Tor Vergata, January 2016) for the invitation and the hospitality. He is also indebted with “abx”, “aglearner”, Ariyan Javanpeykar, Stefan Behrens and Mohan Ramachandran for interesting discussions on several MathOverflow threads, with R. Pardini and V. Coti Zelati for their support during the editing process and with the anonymous referee for helpful comments and remarks.

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Copyright information

© Unione Matematica Italiana 2017

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversità della CalabriaArcavacata di RendeItaly

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