Dirichlet fundamental domains and topology of projective varieties. (English) Zbl 1348.20045
Summary: We prove that for every finitely-presented group \(G\) there exists a 2-dimensional irreducible complex-projective variety \(W\) with the fundamental group \(G\), so that all singularities of \(W\) are normal crossings and Whitney umbrellas.
MSC:
| 20F65 | Geometric group theory |
| 57M05 | Fundamental group, presentations, free differential calculus |
| 14B05 | Singularities in algebraic geometry |
| 14J17 | Singularities of surfaces or higher-dimensional varieties |
| 14F35 | Homotopy theory and fundamental groups in algebraic geometry |
Keywords:
finitely presented groups; irreducible complex projective varieties; fundamental groups; singularities; normal crossings; Whitney umbrellasReferences:
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