Construction of surfaces of general type from elliptic surfaces via Q-Gorenstein smoothing

2010/08/06 by JongHae Keum, Keum, JongHae, Yongnam Lee +3
Mathematics · #14J10 (Secondary) #14J17 #14J29 (Primary) #53D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Geometric Topology (math.GT) #math.AG #math.GT #msc:14J10 #msc:14J17 #msc:14J29 #msc:53D05

paper · pdf · doi:10.48550/arxiv.1008.1222

This paper combines two preprints arXiv:1008.1222 and arXiv:0910.3476. The results are slightly improved

openalex publication_date 2010/08/06 · arxiv created 2010/11/18 · arxiv updated 2010/11/19 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We present methods to construct interesting surfaces of general type via ℚ-Gorenstein smoothing of a singular surface obtained from an elliptic surface. By applying our methods to special Enriques surfaces, we construct new examples of a minimal surface of general type with p_g=0, π₁=ℤ/2ℤ, and K²≤ 4.

Citations

• A complex surface of general type with p_g=0, K²=4, and π₁=ℤ/2ℤ
• The classification of minimal product-quotient surfaces with p_g=0

Related

• Surfaces of general type with p_g=1 and q=0
• A simply connected surface of general type with p_g=1, q=0, and K²=8
• A construction of Horikawa surface via Q-Gorenstein smoothings
• A complex surface of general type with p_g=0, K²=3 and H₁=Z/2Z
• A simply connected surface of general type with p_g=0 and K²=4