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9
votes
1
answer
3k
views
blow-up along singular variety
Can somebody give me a nice example of blow-up of a smooth algebraic variety along a singular subvariety? Something I can do some exercise on and check the differences with a smooth blow-up. Thanks!
7
votes
1
answer
459
views
kapranov's realization of $\overline{M}_{0,n}$ over other fields
Kapranov gave a very nice desciption, over $\mathbb{C}$ of the moduli space of stable pointed rational curves $\overline{M}_{0,n}$ as a series of blow-ups of $P^{n-3}$. Does this, or a similar result, …
3
votes
2
answers
331
views
blow up of segre primal and $\mathcal{M}_{0,6}$
The segre cubic primal $X\subset P^4$ is the GIT quotient of 6 points on $P^1$. Let $M_{0,6}$ the DM compactification of the moduli of 6-pointed rational curves. The Segre primal $X$ is a cubic 3-fold …
1
vote
0
answers
164
views
Cohomology of a stratified projective bundle
Let $S$ be a smooth algebraic variety, and suppose $X\to S$ is a smooth morphism of schemes such that the geometric fibers are all projective spaces. Let us suppose that the dimension of the fibers is …