# Need explanation for $CY_3$ folds comes first rather than algebraic curves comes first [duplicate]

The example I am aware of so far is quintic 3-fold equipped with $SU(3)$ holonomy. Why it is more natural to talk about $CY_3$ folds or Calibi-Yau 3 folds without talking about algebraic curves in string theory? Why it is not more natural to talk about curves first? Or why it is more intuitive to movtivate 3-fold first rather than motivate algebraic curves? Reminder: This is not a popular science question. I need mathematical and theoretical physics justification. Please give me the reference if possible.