Normal quintic surfaces with Kodaira dimension one

摘要

We study normal quintic surfaces in the three-dimensional projective space whose nonsingular models are surfaces of Kodaira dimension one. It turns out that the genus of the base curve of their elliptic fibration is equal to 0 or 1, and the possible values of other invariants of these surfaces and the singularities on them are obtained. We give several examples to show the existence of such surfaces. Moreover we determine the defining equations of general quintic surfaces whose nonsingular models are irregular elliptic surfaces of Kodaira dimension one.