Flat deformations of ${\mathbb P}^n$
  In this paper we study projective flat deformations of projective spaces. We prove that the singular fibers of projective flat deformations of projective spaces appear either in codimension 1 or over singular points of the base. We also describe projective flat deformations of projective spaces with smooth total space, and discuss flatness criteria. 
Carolina Araujo and Jos\'e J. Ram\'on-Mar\'i
math.AG