3 problems

Let $X$ be a smooth projective variety of dimension $d$ over an algebraically closed field $\kappa$, and let $L$ be a big line bundle on $X$. For each valuation $\nu$ in the higher…

Let $X$ be a projective variety of dimension $d$, let $L$ be a big line bundle on $X$, and let $D$ be a simple normal crossing divisor whose dual cone complex $\Sigma(D)$ is pure o…

Higher rank valuations take values in lexicographically ordered groups, and their associated higher rank skeleta arise as tangent cones of dual cone complexes. For a big line bundl…