2 problems

Trailing-term exponent conjecture. Every such $r$-separated $n$-tuple appears as one of the trailing-term exponents of a polynomial corresponding to a section of $L_n\otimes E^r$.

Global sections cone conjecture. Assume that the zip datum ${\mathcal Z}$ is of connected-Hodge-type, that for every connected component $X^\circ\subset X$ the map…