8 problems

Let $S$ be a smooth surface embedded in ${\bf P}^{6}$ with no trisecant lines. The authors construct a list of such surfaces, including cases with and without lines, and distinguis…

Let $p$ be a prime, let $q=p^e$, and let $k$ be a field extension of $\mathbb F_{q^2}$. Consider the Fermat surface in $\mathbb P^3(k)$ defined by … It contains $q^4+q^3+q+1$ lines…

Let $m\geq 4$, and let $X'\subset\mathbb P^{3m-1}$ be the companion surface, of degree $(m+1)^2$, arising as the image of the map $\psi$ described in the source. Let $h$ denote its…

Let $m\geq 4$, and let $\bar X$ be the projected surface described in the preceding construction. Its Hilbert $h$-vector is denoted by $h$. Conjectural h-vector. Computations with…

A noncommutative projective surface is a connected graded noetherian domain of Gelfand–Kirillov dimension three, considered up to its associated noncommutative projective scheme. A…

Equality conjecture. The spaces are equal:

Let $X$ be a smooth complex projective surface and let $v\in N(X)$. Consider the space of good Bridgeland stability conditions for $v$, together with the boundary of its closure, a…

Let ${\mathbb D} = (X, \mathcal{L}, \sigma, \mathcal{A}, \mathcal{D}, \mathcal{C},s)$ be transverse ADC data, and let $T:= T({\mathbb D})$. The category $\operatorname{Qgr-\!} T$ i…