The minimal genus problem in $\mathbb{C\mskip-1mu P}^2 \mathbin{\#} \mathbb{C\mskip-1mu P}^2$

Abstract

In this paper, we give two infinite families of counterexamples and finite positive examples to a conjecture on the minimal genus problem in ${ℂ\mathbb{P}}^2\#{ℂ\mathbb{P}}^2$ proposed by Lawson [Exposition. Math. 15 (1997) 385–431].