2012/09/30 by Jan Stevens
Mathematics · #Bundle #Complex manifold #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #Hypersurface #Manifold (fluid mechanics) #Resolution (logic) #Singularity #Type (biology) #math.AG #math.CV #msc:13C20 #msc:14E30 #msc:32F10 #msc:32Q15 #msc:32S45 #msc:32T15
paper · pdf · doi:10.5802/aif.2909
published as Ann. Inst. Fourier 64 (2014), 2205-2222 · 16 pages, 2 figures changes following referee report; some wrong formulas corrected
arxiv created 2013/11/11 · openalex publication_date 2014/01/01 · arxiv updated 2018/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> </mml:math> -convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . To this end we study small resolutions of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>c</mml:mi> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:math> -singularities.