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Numerical properties of exceptional divisors of birational morphisms of smooth surfaces

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Abstract

We make a very detailed analysis of effective divisors whose support is contained in the exceptional locus of a birational morphism of smooth projective surfaces. As an application we extend Miyaoka’s inequality on the number of canonical singularities on a projective normal surface with non-negative Kodaira dimension to the non minimal case, obtaining a slightly better result than known extensions by Megyesi and Langer.

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Acknowledgements

We are indebted to the referee for useful suggestions, in particular for pointing out the references [5] and [8].

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior de Economia e Gestão, Universidade de Lisboa, R. do Quelhas, 1200-781, Lisbon, Portugal

    Vicente Lorenzo

  2. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Margarida Mendes Lopes

  3. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, 56127, Pisa, Italy

    Rita Pardini

Authors
  1. Vicente Lorenzo
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  2. Margarida Mendes Lopes
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  3. Rita Pardini
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Correspondence to Margarida Mendes Lopes.

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V.L. was partially supported by FCT/Portugal through the program Lisbon Mathematics PhD, scholarship FCT - PD/BD/128421/2017.

M.M.L. was partially supported by FCT/Portugal through Centro de Análise Matemática, Geometria e Sistemas Dinâmicos (CAMGSD), IST-ID, projects UIDB/04459/2020 and UIDP/04459/2020.

R.P. was partially supported by the project PRIN 2017SSNZAW_004 “Moduli Theory and Birational Classification” of Italian MIUR and is a member of GNSAGA of INDAM.

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Lorenzo, V., Mendes Lopes, M. & Pardini, R. Numerical properties of exceptional divisors of birational morphisms of smooth surfaces. Rend. Circ. Mat. Palermo, II. Ser 72, 2363–2374 (2023). https://doi.org/10.1007/s12215-022-00803-1

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  • DOI: https://doi.org/10.1007/s12215-022-00803-1

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