The Halphen cubics of order two

Autores: Thomas Bauer, Brian Harbourne, Joaquim Roé Vellvé , Tomasz Szemberg
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 3, 2017, págs. 339-357
Idioma: inglés
DOI: 10.1007/s13348-016-0172-4
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Resumen
- For each ?⩾1 , Roulleau and Urzúa give an implicit construction of a configuration of 4(3?2−1) 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 ?=1 (which were known) and for ?=2 (which are new).