Two examples of surfaces with normal crossing singularities

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This note gives two examples of surfaces with normal crossing singularities. In the first example the canonical ring is not finitely generated. In the second, the canonical line bundle is not ample but its pull back to the normalization is ample. The latter answers in the negative a problem left unresolved in III. 2.6.2 of Éléments de géometrie algébrique, 1961, and raised again by Viehweg.

Original languageEnglish (US)
Pages (from-to)1707-1712
Number of pages6
JournalScience China Mathematics
Issue number8
StatePublished - Aug 2011

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • ampleness criteria
  • canonical ring
  • singular surface


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