## New answers tagged intersection-theory

0
votes

### Number of intersection points of a system of quartic polynomials induced by the projected matrix commutator

When $r = 1$, any unit vector $V_r$ satisfies the equations, not just eigenvectors of $A$ and $B$. This disproves the conjecture.

6
votes

### Negative intersection number between curve and effective divisor

If $X$ is a smooth projective variety of dimension $d$ and $\tilde X \to X$ is the blowup of $X$ at a point $x$, then the exceptional divisor $E \subseteq \tilde X$ is isomorphic to $\mathbf P^{d-1}$ ...

5
votes

### Negative intersection number between curve and effective divisor

It is not. Let $X$ be a smooth surface and let $X^{[n]}$ be the Hilbert scheme of $n$ points on $X$, parameterizing zero-dimensional subschemes of $X$ of length $n$ . This is a smooth complex ...

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