Abstract
In this paper we solve the problem proposed by Xiao about the existence of surfaces with p g = 4, K 2 X = 9 and canonical map composed with a pencil [X4]. In fact we show that such surfaces do not exist. As a consequence of our non-existence result we obtain the new bound K 2 X ≥ 4 p g − 6 where X is a minimal surface of general type with canonical map composed with a pencil and p g ( X) ≥ 3.
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