In this paper we solve the problem proposed by Xiao about the existence of surfaces with pg = 4, K2X = 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 K2X ≥ 4pg - 6 where X is a minimal surface of general type with canonical map composed with a pencil and pg(X) ≥ 3.
Numerical inequalities for surfaces with canonical map composed with a pencil
ZUCCONI, Francesco
1998-01-01
Abstract
In this paper we solve the problem proposed by Xiao about the existence of surfaces with pg = 4, K2X = 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 K2X ≥ 4pg - 6 where X is a minimal surface of general type with canonical map composed with a pencil and pg(X) ≥ 3.File in questo prodotto:
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