SEOUL – South Korea has spent billions of dollars on policies to boost its birthrate. But when Kim Kyu-jin and her wife wanted to have a baby, they had to fly to Belgium. Legally, South Korea considers Kim single, despite her 2019 wedding — ceremony in Seoul, legal registration in New York City — because the country does not recognize same-sex unions. Seoul city authorities declined to register her marriage. So when the happy couple decided they were ready to have a baby, their domestic options were limited: single people are typically deemed ineligible to adopt and sperm banks are designed for heterosexual married couples with fertility issues. But Kim Kyu-jin and her wife Kim Sae-yeon — they share the same last name by coincidence — decided to try anyway and, thanks to in vitro fertilization (IVF) using donor sperm in Belgium, Kyu-jin is now eight months pregnant.