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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

3 votes
1 answer
187 views

snc singularity is an open condition?

If $π : X → S$ is a family of complex projective varieties, such that $X_0 := π^{−1}(0)$ has simple normal singularities in $X$, then all the general fibers $X_t$ have snc singularities at worst?
Helen's user avatar
  • 135
3 votes
1 answer
714 views

semi-log canonial singularities is an open condition?

Let $f:X\to \mathbb \Delta$ be family of projective varities which fibers are smooth, we know central fiber can be singular and may not be mild. Kollar introduced semi-log-canonical singularities to g …
Helen's user avatar
  • 135
7 votes
1 answer
887 views

If monodromy representation is unipotent then special fiber is snc?

We know, if $π : X → S$ is a generically smooth family of complex projective varieties, such that $X_0 := π^{−1}(0)$ is an snc divisor in $X$, then the monodromy representation is unipotent. Now assum …
Helen's user avatar
  • 135