Log canonical models of elliptic surfaces
Abstract
We give a classification of the log canonical models of elliptic surface pairs consisting of an elliptic fibration, a section, and a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of the weights. We describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes. In addition, we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers. This is the first step in constructing compactifcations of moduli spaces of elliptic surfaces using the minimal model program.
 Publication:

arXiv eprints
 Pub Date:
 October 2016
 arXiv:
 arXiv:1610.08033
 Bibcode:
 2016arXiv161008033A
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 Some notational changes and citations added. Version to appear in Advances in Mathematics