Skip to main content
added 45 characters in body
Source Link
Daniel Loughran
  • 21.4k
  • 3
  • 46
  • 136

Let $X$ be a smooth projective rationally connected variety over $\mathbb{C}((t))$ and $R= \mathbb{C}[[t]].$

Does there exist a proper regular scheme $\mathcal{X} \to \mathrm{Spec}(R)$ whose special fibre is reduced and whose generic fibre is isomorphic to $X$? I.e. the special fibre is a sum of divisors on $\mathcal{X}$, and I want there to be no multiple components appearing.

Let $X$ be a smooth projective rationally connected variety over $\mathbb{C}((t))$ and $R= \mathbb{C}[[t]].$

Does there exist a proper regular scheme $\mathcal{X} \to \mathrm{Spec}(R)$ whose special fibre is reduced? I.e. the special fibre is a sum of divisors on $\mathcal{X}$, and I want there to be no multiple components appearing.

Let $X$ be a smooth projective rationally connected variety over $\mathbb{C}((t))$ and $R= \mathbb{C}[[t]].$

Does there exist a proper regular scheme $\mathcal{X} \to \mathrm{Spec}(R)$ whose special fibre is reduced and whose generic fibre is isomorphic to $X$? I.e. the special fibre is a sum of divisors on $\mathcal{X}$, and I want there to be no multiple components appearing.

Source Link
Daniel Loughran
  • 21.4k
  • 3
  • 46
  • 136

Degenerations of rationally connected varieties

Let $X$ be a smooth projective rationally connected variety over $\mathbb{C}((t))$ and $R= \mathbb{C}[[t]].$

Does there exist a proper regular scheme $\mathcal{X} \to \mathrm{Spec}(R)$ whose special fibre is reduced? I.e. the special fibre is a sum of divisors on $\mathcal{X}$, and I want there to be no multiple components appearing.