Genetic contributions to human cortical structure manifest pervasive pleiotropy. This pleiotropy may be harnessed to identify unique genetically-informed parcellations of the cortex that are neurobiologically distinct from functional, cytoarchitectural, or other cortical parcellation schemes. We investigated genetic pleiotropy by applying genomic structural equation modeling (SEM) to map the genetic architecture of cortical surface area (SA) and cortical thickness (CT) for the 34 brain regions recently reported in the ENIGMA cortical GWAS. Genomic SEM uses the empirical genetic covariance estimated from GWAS summary statistics with LD score regression (LDSC) to discover factors underlying genetic covariance, which we are denoting genetically informed brain networks (GIBNs). Genomic SEM can fit a multivariate GWAS from summary statistics for each of the GIBNs, which can subsequently be used for LD score regression (LDSC). We found the best-fitting model of cortical SA identified 6 GIBNs and CT identified 4 GIBNs. The multivariate GWASs of these GIBNs identified 74 genome-wide significant (GWS) loci (p<5×10-8), including many previously implicated in neuroimaging phenotypes, behavioral traits, and psychiatric conditions. LDSC of GIBN GWASs found that SA-derived GIBNs had a positive genetic correlation with bipolar disorder (BPD), and cannabis use disorder, indicating genetic predisposition to a larger SA in the specific GIBN is associated with greater genetic risk of these disorders. A negative genetic correlation was observed with attention deficit hyperactivity disorder (ADHD), major depressive disorder (MDD), and insomnia, indicating genetic predisposition to a larger SA in the specific GIBN is associated with lower genetic risk of these disorders. CT GIBNs displayed a negative genetic correlation with alcohol dependence. Jointly modeling the genetic architecture of complex traits and investigating multivariate genetic links across phenotypes offers a new vantage point for mapping the cortex into genetically informed networks.