A complex surface of general type with p_g=0, K^2=2 and H_1=Z/2Z, Z/3Z
Yongnam Lee (Sogang U.), Jongil Park (Seoul National U.)
TL;DR
This paper constructs new complex surfaces of general type with specific invariants p_g=0, K^2=2, and fundamental groups Z/2Z and Z/3Z, using advanced surgical and smoothing techniques.
Contribution
It introduces explicit constructions of minimal complex surfaces with prescribed invariants and fundamental groups, expanding the known examples in algebraic geometry.
Findings
Constructed a surface with H_1=Z/2Z
Provided an example with H_1=Z/3Z
Applied rational blow-down and Q-Gorenstein smoothing methods
Abstract
As the sequel to [3], we construct a minimal complex surface of general type with p_g=0, K^2=2 and H_1=Z/2Z using a rational blow-down surgery and Q-Gorenstein smoothing theory. We also present an example of p_g = 0,K^2 = 2 and H_1 = Z/3Z.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Meromorphic and Entire Functions · Geometric Analysis and Curvature Flows