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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
2
votes
1
answer
158
views
On linear sections of a nonsingular threefold
Let $X$ be a nonsingular threefold of degree $d$ contained in $\mathbb{P}^4$ and let $P$ be a point on $X$. Is it possible to find a plane $H$ contained in $T_P (X)$ such that $X \cap H$ is not a unio …
1
vote
0
answers
193
views
Classifications of cubic surfaces
Is there a known classification of singular cubic surfaces over finite fields?
1
vote
2
answers
318
views
Does there exist a surface over a finite field which contains three skew lines?
Does there exist an irreducible surface, other than Hermitian surface, in $\mathbb{P}^3 (\mathbb{F}_q)$ containing three skew lines?
I know that this is true for Hermitian surface. In fact, at every …