Algebraic surfaces with p(g) bold= /boldq bold= /bold1, K-2 bold= /bold4 and genus 3 Albanese fibration

摘要

In this paper, we study the Gieseker moduli space M-1,1(4,3) of minimal surfaces with p(g) = q = 1, K-2 = 4 and genus 3 Albanese fibration. Under the assumption that direct image of the canonical sheaf under the Albanese map is decomposable, we find two irreducible components of M-1,1(4,3), one of dimension 5 and the other of dimension 4.