A simply connected surface of general type with p_g=0 and K^2=3

Abstract

Motivated by a recent result of Y. Lee and the second author[7], we construct a simply connected minimal complex surface of general type with p_g=0 and K^2=3 using a rational blow-down surgery and Q-Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic 4-manifold with b_2^+=1 and K^2=4.Comment: 17 pages, 10 figures, a section regarding a symplectic 4-manifold with K^2=4 is adde