6 problems

Consider a four-dimensional theory described by a genus-$g$ fiberation with one special singular fiber $F_\infty$ at $z=\infty$, only $A_1$ singularities in the bulk, and, in the h…

Generalized local-signature conjecture. The quantity $h_x$ equals $d_x-\delta_x$ not only in the rank-one and rank-two cases, but for the general case. The quantity $h_x$ measures…

Let $f\colon F\to Y$ be a Harris–Morrison genus-$g$ fibration with maximal gonality $k$, meaning $k=\frac{g+3}{2}$ if $g$ is odd and $k=\frac{g+2}{2}$ if $g\geq 4$ is even. Let…

Let $s$ and $n$ denote the numbers of separating and non-separating vanishing cycles, respectively, in a genus $2$ Lefschetz fibration. Suppose that … For such fibrations, write th…

Let ${\cal CY}_B^3$ be the set of triples $(X,f,B)$ where $X$ is a normal projective threefold with only canonical singularities, $K_X$ is numerically trivial, and…

Let $f:X\rightarrow B$ be a proper surjective morphism from a normal algebraic threefold $X$ onto $B\simeq \mathbb{P}^1$, whose general fibre is a surface with Kodaira dimension ze…