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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.
2
votes
Linear equivalence and Hilbert function
Let me show that the answer to this question is positive for $d>3$. Indeed, for a general surface $X$ of degree $d>3$ its Picard group is $\mathbb Z$
and is generated by $O(1)$. It follows that both c …
14
votes
Accumulation of algebraic subvarieties: Near one subvariety there are many others (?), 2
One little counterexample (to both versions of the question). On a quintic $3$-fold in $\mathbb CP^4$ there are $2875$ lines. You can take any of these lines. An analytic neighbourhood of such a line …
7
votes
Looking for a particular family of C.Y quintics
Let me say first, that I really like this question. Very unusual question about such well known things (in fact I did not know even that the real quintic $\sum_i x_i^5=0$ is $\mathbb RP^3$).
This is …
20
votes
Accepted
Accumulation of algebraic subvarieties: Near one subvariety there are many others (?)
The answer is yes (as in the case of Sasha's answer we use ramified covers)
Proof. Let $X$ be any variety in $\mathbb CP^n$. Take a section $s_m$ of $O(m)$ on $X$ such that $s_m$ is not equal to $m$ …