Classifying symmetries of rational elliptic surfaces with section

2010-08-05
This is a complex algebraic geometry talk in which I will discuss how to give a classification of the group of symmetries of rational elliptic surfaces. A rational elliptic surface is the blow up of the projective plane at the 9 base points of a pencil of cubics. Equivalently it is an algebraic surface birational to P 2 which has a map to P 1 with generic fiber an elliptic curve. Singular fibers of this map play an important role in the structure of the group of symmetries of the surface and we can obtain very useful combinatorial information from them to determine this group. The group of symmetries of a rational elliptic surface is simply the semi-direct product of an at most rank 8 abellian group which is known in the literature as the Mordell-Weil group of the surface and a finite group of order at most 24 which is a special subgroup of the group of symmetries defined in terms of the section of the map from the surface to P 1 . The Mordell-Weil group is known for every rational elliptic surface and is determined by the configuration of singular fibers, in my work I am describing the second factor of the semi-direct product structure of the group of symmetries in terms of the singular fibers.
Citation Formats
T. Karayayla, “Classifying symmetries of rational elliptic surfaces with section,” Pittsburgh,PA, Amerika Birleşik Devletleri, 2010, p. 68, Accessed: 00, 2021. [Online]. Available: http://www.maa.org/sites/default/files/pdf/abstracts/mf2010-abstracts.pdf.