Two examples of surfaces with normal crossing singularities

2007/05/07 by Janós Kollár, János Kollár, Kollár, János · 2 citations
Mathematics · Physics and Astronomy · #14C20 #14J10 #14J29 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #math.AG #msc:14C20 #msc:14J10 #msc:14J29

paper · pdf · doi:10.48550/arxiv.0705.0926

Version 2: Several details corrected

openalex publication_date 2007/05/07 · arxiv created 2007/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 [EGA,III.2.6.2] and raised again by Viehweg.

Cited by

• The Calabi conjecture and K-stability
• Singularities of stable varieties

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