3 problems

Let $B_1^n=\operatorname{conv}\{\pm e_1,\ldots,\pm e_n\}$ be the cross-polytope, and let … For $a\in\mathcal{M}$, consider the central hyperplane section $B_1^n\cap a^\perp$. Maxim…

Hyperplane-section conjecture. Under these conditions,

Let $P=\mathbb{P}^N$, and let $X\subset P$ be a general complete intersection of multi-degree $(d_1,d_2,\ldots,d_k)$ with $d_1\leq\cdots\leq d_k$. Assume that $d_1\gg0$. For a hype…