PVC for range hood ventilation
Check your local building codes to be 100% sure but PVC is NOT permitted by many.  I'll reference one from TX but most are similar where it says:


  M1503.2 Duct Material 
  
  Ducts serving range hoods shall be constructed
  of galvanized steel, stainless steel or copper.


Regarding size, I believe you'll find that your local codes also require adhering to the hood manufacturer's specification for duct size.

See: TX Code