A complex surface of general type with p_g=0, K²=2 and H₁=ℤ/4ℤ

2010/12/29 by Heesang Park, Jongil Park, Park, Heesang +5
Computer Science · Mathematics · #14J17 #53D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation #Primary 14J29 #Secondary 14J10 #math.AG #math.GT #msc:14J10 #msc:14J17 #msc:14J29 #msc:53D05

paper · pdf · doi:10.48550/arxiv.1012.5871

24 pages, 25 figures: Simplified the proof of Theorem 5.1; Added Proposition 3.2, Remark 3.3, Remark 6.2 for the ampleness problem; Corrected typos; To appear in Trans. Amer. Math. Soc

openalex publication_date 2010/12/29 · arxiv created 2011/08/25 · arxiv updated 2011/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a new minimal complex surface of general type with p_g=0, K²=2 and H₁=ℤ/4ℤ (in fact π₁^alg=ℤ/4ℤ), which settles the existence question for numerical Campedelli surfaces with all possible algebraic fundamental groups. The main techniques involved in the construction are a rational blow-down surgery and a ℚ-Gorenstein smoothing theory.

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