Skip to main content
2 of 5
edited title
Pete L. Clark
  • 65.4k
  • 12
  • 241
  • 381

Does smooth target space and smooth fibers imply smooth total space?

Suppose that $f: X \rightarrow Y$ is a morphism between algebraic varieties. If $Y$ is smooth, and the fibers of $f$ over closed points of $Y$ are proper and nonsingular, does it follow that $X$ is smooth?

unknown
  • 181
  • 6