Is the number of irreducible components of an irreducible projective variety $V$ over an algebraically closed field with any linear subspace $L$ always least than $\deg(V)$? I think so but I didn't manage to prove it.
2026-03-28 10:56:04.1774695364
Number of irreducible components in an intersection
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Of course. The degree of the intersection is the same as the degree of $V$ so, since any component has at least degree $1$, we can have at most $\deg V$ components, counted with multiplicity.