A construction of Horikawa surface via Q-Gorenstein smoothings
Yongnam Lee (Sogang U.), Jongil Park (Seoul National U.)
TL;DR
This paper demonstrates that the Fintushel-Stern construction of Horikawa surfaces, originally in smooth topology, can be realized within the complex algebraic category using Q-Gorenstein smoothings.
Contribution
It provides a new algebraic geometric construction of Horikawa surfaces via Q-Gorenstein smoothings, bridging smooth and complex categories.
Findings
Construction of Horikawa surfaces in complex category
Application of Q-Gorenstein smoothings in surface construction
Extension of smooth topological methods to algebraic geometry
Abstract
In this article we prove that Fintushel-Stern's construction of Horikawa surface, which is obtained from an elliptic surface via a rational blow-down surgery in smooth category, can be performed in complex category. The main technique involved is Q-Gorenstein smoothings.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models