Hi,

My question seems to be closely related to that one : What strict resolutions of singularities are needed? (and it is perhaps even included in it, but I am not so sure).

Let $X$ be a Gorenstein projective variety with canonical singularities. Does there exist a sequence :

$ X_N \rightarrow ... X_i \rightarrow X_{i-1} ... \rightarrow X_0 = X$ such that:

i) $X_N$ is smooth,

ii) $X_i \rightarrow X_{i-1}$ is the blow up along a smooth subvariety $Z_{i-1} \subset X_{i-1}$

iii) The exceptional divisor of $X_i \rightarrow X_{i-1}$ has only Log-canonical (or perhaps DuBois?) singularities?

Even if Log-canonical or DuBois is impossible, is there any regularity condition one can impose on these exceptional divisors?

Thanks.

Hi,

My question seems to be closely related to that one : What strict resolutions of singularities are needed? (and it is perhaps even included in it, but I am not so sure).

Let $X$ be a Gorenstein projective variety with canonical singularities. Does there exist a sequence :

$ X_N \rightarrow ... X_i \rightarrow X_{i-1} ... \rightarrow X_0 = X$ such that:

i) $X_N$ is smooth,

ii) $X_i \rightarrow X_{i-1}$ is the blow up along a smooth subvariety $Z_{i-1} \subset X_{i-1}$

iii) The exceptional divisor of $X_i \rightarrow X_{i-1}$ has only Log-canonical (or perhaps DuBois?) singularities?

Even if Log-canonical or DuBois is impossible, is there any regularity condition one can impose on these exceptional divisors?

Thanks.

Hi,

My question seems to be closely related to that one : What strict resolutions of singularities are needed? (and it is perhaps even included in it, but I am not so sure).

Let $X$ be a Gorenstein projective variety with canonical singularities. Does there exist a sequence :

$ X_N \rightarrow ... X_i \rightarrow X_{i-1} ... \rightarrow X_0 = X$ such that:

i) $X_N$ is smooth,

ii) $X_i \rightarrow X_{i-1}$ is the blow up along a smooth subavariety $Z_{i-1} \subset X_{i-1}$

iii) The exceptional divisor of $X_i \rightarrow X_{i-1}$ has only Log-canonical (or perhaps DuBois?) singularities?

Even if Log-canonical or DuBois is impossible, is there any regularity condition one can impose on these exceptional divisors?

Thanks.

Hi,

My question seems to be closely related to that one : What strict resolutions of singularities are needed? (and it is perhaps even included in it, but I am not so sure).

Let $X$ be a Gorenstein projective variety with canonical singularities. Does there exist a sequence :

$ X_N \rightarrow ... X_i \rightarrow X_{i-1} ... \rightarrow X_0 = X$ such that:

i) $X_N$ is smooth,

ii) $X_i \rightarrow X_{i-1}$ is the blow up along a smooth subvariety $Z_{i-1} \subset X_{i-1}$

iii) The exceptional divisor of $X_i \rightarrow X_{i-1}$ has only Log-canonical (or perhaps DuBois?) singularities?

Even if Log-canonical or DuBois is impossible, is there any regularity condition one can impose on these exceptional divisors?

Thanks.