Standard isotrivial fibrations with p_g=q=1, II
By E. Mistretta, Francesco Polizzi. 2007
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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 p g = q = 1 have been classified in [F. Polizzi, Standard isotrivial fibrations with p g = 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 p g = q = 1 , K S 2 = 5 and Albanese fibration of genus 3. Finally, we show with explicit examples that the case where S is not minimal actually occurs.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/dbf71009a629238c1e2c628f1fffe2786e4ed2ed
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The classification of isotrivially fibred surfaces with pg = q = 2 (2009, methodology): “Theorem 5.10 [ 14 ] Let S = (C × F)/G be a surface with pg = q = 1 isogenous to a product of curve.”