5 problems

The conjecture on singular loci. The singular locus of a general element of $\mathcal D$ is a disjoint union of such linear spaces $\mathcal T$; in particular, $X$ is swept out by…

Let $M$ and $\hat M$ be generic mirror Calabi–Yau $3$-folds. Suppose there exist special Lagrangian fibrations … Let $\Delta_f\subset B$ and $\Delta_{\hat f}\subset\hat B$ be their…

Let $M$ be an almost Calabi–Yau $3$-fold with a smooth special Lagrangian fibration $f:M\rightarrow B$, and let $\tilde M$ be a small generic deformation of $M$. For the smooth fib…

Let $X^{\natural}$ be the model denoted $X^{\natural}(4,2)$, with discriminant $\Delta$ and large-volume divisors $D_{1}$ and $D_{2}$. Let $\mathfrak L_{m}^{(1)}$ denote the corres…

Let $V_k$ be the locus of cubic surfaces for which the matrix $M$ has rank at most $20-k$, and let $N_2$ denote the locus of binodal cubic surfaces. The $19\times 19$ minors of $M$…