We classify the minimal surfaces of general type with K^2 <= 4chi - 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 chi >> 0, 4 chi - 10 <= K^2 <= 4 chi - 8. All these surfaces are complete intersections in a toric 4-fold and bidouble covers of Hirzebruch surfaces. The surfaces with K^2 = 4 chi - 8 were previously constructed by Catanese as bidouble covers of P^1 x P^1.
On surfaces with a canonical pencil
Pignatelli, Roberto
2012-01-01
Abstract
We classify the minimal surfaces of general type with K^2 <= 4chi - 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 chi >> 0, 4 chi - 10 <= K^2 <= 4 chi - 8. All these surfaces are complete intersections in a toric 4-fold and bidouble covers of Hirzebruch surfaces. The surfaces with K^2 = 4 chi - 8 were previously constructed by Catanese as bidouble covers of P^1 x P^1.File in questo prodotto:
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