发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明终端和典范 Gorenstein Fano 四折叠的反典范体积上界，并给出尖锐界及特殊情形下的改进。
AI 中文摘要
设 $X$ 为 Picard 数为一的复 $\mathbb{Q}$-因子 Gorenstein Fano 四折叠。我们证明，若 $X$ 具有终端奇点，则 $(-K_X)^4\le648$，等号恰在 $\mathbb{P}(1,1,1,1,2)$ 时成立。若奇点为典范，我们得到 $(-K_X)^4\le7332$。在附加假设一个原始 Weil 极化在有限多个点之外是 Cartier 的条件下，后一界改进为尖锐界 $1024$；若其非 Cartier 轨迹维数至多为一，我们得到 $6084$。
英文摘要
Let $X$ be a complex $\mathbb{Q}$-factorial Gorenstein Fano fourfold of Picard number one. We prove that, if $X$ has terminal singularities, then $(-K_X)^4\le648$, with equality precisely for $\mathbb{P}(1,1,1,1,2)$. If the singularities are canonical, we obtain $(-K_X)^4\le7332$. Under the additional assumption that a primitive Weil polarization is Cartier outside finitely many points, the latter bound improves to the sharp bound $1024$; if its non-Cartier locus has dimension at most one, we obtain $6084$.
Comments31 pages; comments are welcome!
