The Halphen cubics of order two
Bauer, Thomas (Philipps-Universität Marburg (Alemanya). Fachbereich Mathematik und Informatik)
Harbourne, Brian (University of Nebraska (Estats Units d'Amèrica). Department of Mathematics)
Roé Vellvé, Joaquim (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Szemberg, Tomasz

Data:	2016
Resum:	For each m⩾1, Roulleau and Urzúa give an implicit construction of a configuration of 4(3m2−1) complex plane cubic curves. This construction was crucial for their work on surfaces of general type. We make this construction explicit by proving that the Roulleau-Urzúa configuration consists precisely of the Halphen cubics of order m, and we determine specific equations of the cubics for m=1 (which were known) and for m=2 (which are new).
Ajuts:	Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-114 Ministerio de Ciencia e Innovación 2013/40680-P
Nota:	Agraïments: The understanding necessary for this paper grew out of discussions that occurred in working groups at two workshops in 2015, namely "Recent advances in Linear series and Newton-Okounkov bodies", February 9-14 at the University of Padua, and "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems", February 15-21 at the Mathematisches Forschungsinstitut Oberwolfach. We thank the participants in these workshops and the institutions that hosted them. We also thank the University of Freiburg for hosting visits by Bauer and Harbourne to work on this paper with Szemberg in person for a week in the summer of 2015. In addition, the research of Bauer was partially supported by DFG grant BA 1559/6-1. The research of Szemberg was partially supported by National Science Centre, Poland, Grant 2014/15/B/ST1/02197.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Automorphisms ; Abelian surfaces ; Halphen cubics ; Hesse arrangement ; Rational surfaces
Publicat a:	Collectanea mathematica, 2016 , ISSN 0010-0757

DOI: 10.1007/s13348-016-0172-4

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