##  [Blow-Up (Algebraic Geometry)](/blow-algebraic-geometry) 

  ##  [Blow-Up (Algebraic Geometry)](https://mathlogic.quantumdictionary.io/blow-algebraic-geometry-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A birational geometric operation that replaces a chosen subvariety by its projectivized normal directions (the exceptional divisor), modifying the local structure to separate tangents and often to resolve or reduce singularities.