• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.1927-1933
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• 2017

We prove that there are rational homology balls $B_p$ smoothly embedded in the 2-handlebodies associated to certain knots. Furthermore we show that, if we rationally blow up the 2-handlebody along the embedded rational homology ball $B_p$, then the resulting 4-manifold cannot be obtained just by a sequence of ordinary blow ups from the 2-handlebody under a certain mild condition.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1293-1308
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• 2016

In this paper we prove the existence of rational homology balls smoothly embedded in regular neighborhoods of certain linear chains of smooth 2-spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.419-437
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• 2021

We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic varieties.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1269-1274
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• 2010

As the sequel to our previous work [4], we construct a minimal complex surface of general type with $p_g=0$, $K^2=3$ and $H_1$ = $\mathbb{Z}/2\mathbb{Z}$ by using a rational blow-down surgery and $\mathbb{Q}$-Gorenstein smoothing the-ory.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.479-494
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• 2017

We construct various examples of simply connected minimal complex surfaces of general type with $p_g=0$ and $K^2=1,2$ using ${\mathbb{Q}}$-Gorenstein smoothing method.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.493-507
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• 2013

We construct a new family of simply connected minimal complex surfaces of general type with $p_g$ = 1, $q$ = 0, and $K^2$ = 3, 4, 5, 6, 8 using a $\mathbb{Q}$-Gorenstein smoothing theory.