A smooth, projective surface S is called a standard isotrivial fibration if there exists a finite group G which acts faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T := (C × F )/G. Standard isotrivial fibrations of general type with pg = q = 1 have been classified in [F. Polizzi, Standard isotrivial fibrations with pg = q = 1, J. Algebra 321 (2009),1600–1631] under the assumption that T has only Rational Double Points as singularities. In the present paper we extend this result, classifying all cases where S is a minimal model. As a by-product, we provide the first examples of minimal surfaces of general type with pg = q = 1, K^2 = 5 and Albanese fibration of genus 3. Finally, we show with explicit examples that the case where S is not minimal actually occurs.
Standard isotrivial fibrations with p(g) = q=1, II
MISTRETTA, ERNESTO CARLO;
2010
Abstract
A smooth, projective surface S is called a standard isotrivial fibration if there exists a finite group G which acts faithfully on two smooth projective curves C and F so that S is isomorphic to the minimal desingularization of T := (C × F )/G. Standard isotrivial fibrations of general type with pg = q = 1 have been classified in [F. Polizzi, Standard isotrivial fibrations with pg = q = 1, J. Algebra 321 (2009),1600–1631] under the assumption that T has only Rational Double Points as singularities. In the present paper we extend this result, classifying all cases where S is a minimal model. As a by-product, we provide the first examples of minimal surfaces of general type with pg = q = 1, K^2 = 5 and Albanese fibration of genus 3. Finally, we show with explicit examples that the case where S is not minimal actually occurs.Pubblicazioni consigliate
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