Skip to main content
MathOverflow

Return to Question

Forgot an important hypothesis
Source Link
Nicolas Hemelsoet
Nicolas Hemelsoet
  • 768
  • 2
  • 6
  • 15

Consider ana proper algebraic map between complex varieties $f : X \to D$ ($D$ is the unit disk), which is a submersion over $D^*$. I would like to know if they are any condition on $f$ such that the specialisation map $H^*(X_0) \to H^*(X)$ is injective ?

Consider an algebraic map between complex varieties $f : X \to D$ ($D$ is the unit disk), which is a submersion over $D^*$. I would like to know if they are any condition on $f$ such that the specialisation map $H^*(X_0) \to H^*(X)$ is injective ?

Consider a proper algebraic map between complex varieties $f : X \to D$ ($D$ is the unit disk), which is a submersion over $D^*$. I would like to know if they are any condition on $f$ such that the specialisation map $H^*(X_0) \to H^*(X)$ is injective ?

Source Link
Nicolas Hemelsoet
Nicolas Hemelsoet
  • 768
  • 2
  • 6
  • 15

Vanishing cycles and injectivity of the specialisation map

Consider an algebraic map between complex varieties $f : X \to D$ ($D$ is the unit disk), which is a submersion over $D^*$. I would like to know if they are any condition on $f$ such that the specialisation map $H^*(X_0) \to H^*(X)$ is injective ?