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4
votes
Intersection of Subspaces with $O(3)$
In general the answer is no. For example, the matrices whose first column is a column of zeroes form a $6-$dimensional subspace not containing any ortogonal matrix, because it does not contain any inv …
5
votes
Accepted
Does $h^1(D)=0$ imply numerical connectedness on K3 surfaces?
Interesting question. I think the answer is yes, let me try to prove it.
As you noticed, the ideal sheaf sequence shows that $h^1(D)=0$ is equivalent to the fact that $H^0({\mathcal O}_D)$ is 1-dimen …