On surfaces with a canonical pencil

الأصل · EN

We classify the minimal surfaces of general type with K² ≤ 4χ-8 whose canonical map is composed with a pencil, up to a finite number of families. More precisely we prove that there is exactly one irreducible family for each value of χ≫ 0, 4χ-10 ≤ K² ≤ 4χ-8. All these surfaces are complete intersections in a toric 4-fold and bidouble covers of Hirzebruch surfaces. The surfaces with K²=4χ-8 were previously constructed by Catanese as bidouble covers of ¹ × ¹.