it is well known that the extremal rays in the cone of effective curve classes on a k3 surface are generated by rational curves $c$ for which $(c,c)=-2$; a natural question to ask is whether there is a similar characterization for a higher-dimensional holomorphic symplectic variety $x$. the intersection form is no longer a quadratic form on curve classes, but the beauville-bogomolov form on $x$ induces a canonical nondegenerate form $(\cdot,\cdot)$ on $h_2(x;\mathbb{r} )$ which coincides with the intersection form if $x$ is a k3 surface. we therefore might hope that extremal rays of effective curves in $x$ are generated by rational curves $c$ with $(c,c)=-c$ for some positive rational number $c$. in particular, if $x$ contains a lagrangian hyperplane $\mathbb p^n\subset x$, the class of the line $\ell\subset\mathbb p^n$ is extremal. for $x$ deformation equivalent to the hilbert scheme of $n$ points on a k3 surface, hassett and tschinkel conjecture that $(\ell,\ell)=-\frac{n+3}{2}$; this has been verified for $n<4$. in joint work with andrei jorza, we prove the conjecture for $n=4$, and discuss some general properties of the ring of hodge classes on $x$.