All Questions
9 questions
0
votes
1
answer
257
views
Definition of canonical pair
Let $(X,D)$ be a pair and $f:Y\rightarrow X$ a log resolution. Write
$$
K_Y + \widetilde{D} = f^{*}(K_X) + \sum_{i}a_iE_i
$$
where $\widetilde{D}$ is the strict transform of $D$. I found the following ...
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1
vote
1
answer
241
views
Surfaces with rational double points
Let $S\rightarrow \mathbb{P}^1$ a surface fibered in conics over a field. Assume that $S$ has a single non reduced fiber $F$ with two points of type $A_1$ on it.
Blowing-up the two points and ...
- 8,998
6
votes
2
answers
753
views
Smooth complete intersections
Let $X_{2,3}\subset\mathbb{P}^n$, with $n\geq 5$, be a complete intersection of a quadric $X_2$ and a cubic $X_3$ containing a $2$-plane $H$. Assume $X_2$ and $X_3$ to be general among the ...
- 8,998
3
votes
1
answer
175
views
Singularities of surfaces fibered in rational curves
Let $S$ be a projective surface with a morphism $S\rightarrow\mathbb{P}^1$ whose fibers are either smooth $\mathbb{P}^1$'s or the union of two smooth $\mathbb{P}^1$'s intersecting in a point.
...
- 8,998
3
votes
0
answers
171
views
Blowing-up a non reduced fiber
Let $X\rightarrow \mathbb{P}^2$ be a smooth conic bundle with a non reduced fiber $F$, and $\widetilde{X}$ the blow-up of $X$ along $F$ with exceptional divisor $F\times\mathbb{P}^1$.
I expect $\...
- 8,998
3
votes
0
answers
199
views
Divisorial contractions and singularities
I have a smooth $6$-fold $X\subset\mathbb{P}^n$ and a divisor $D\subset X$ cut out by a quadratic polynomial. I know that $D$ in singular along a smooth $3$-fold $Y\subset X$, and that if $Z$ is the ...
user125056
4
votes
1
answer
327
views
Singularities of fibrations
Let $f:X\rightarrow \mathbb{P}^2$ be a fibration, here $X$ is a projective variety of dimension three.
Assume that there exixts a smooth curve $C\subset\mathbb{P}^2$ such that for any $p\in\mathbb{P}...
- 8,998
2
votes
1
answer
167
views
Singularities of $3$-folds
Let $X,Y,Z$ be projective $3$-folds. Assume that $Y$ is smooth and $Z$ is smooth and Fano. Moreover, assume that there is a generically finite morphism $f:Y\rightarrow Z$ admitting a factorization $f=...
user97096
3
votes
0
answers
82
views
Singularities of fibrations 2
This question is related to my previous question:
Singularities of fibrations
Assume that $X$ is a complete intersection irreducible $3$-fold in a product of projective spaces. So that $X$ is ...
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