单有理法诺三维簇
Unirational Fano threefolds
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中文总结 AI 辅助
本文运用Cheltsov等人的相对阿贝尔-雅可比构造，得到50维单有理次数1德尔佩佐三维簇族，构造了两类单有理三维簇的显式单参数族，并重新阐释了双二次三维簇的Roth--Iskovskikh单有理性构造。
中文摘要 AI 辅助
我们运用Cheltsov--Loginov--Orlov--Prokhorov的相对阿贝尔-雅可比构造研究单有理法诺三维簇，主要成果为得到50维的光滑单有理次数1的德尔佩佐三维簇族；还构造了终端单有理六次双固体和皮卡秩1的四次三维簇的显式单参数族；最后通过相对阿贝尔-雅可比映射诱导的对应关系，重新阐释了光滑双二次三维簇的Roth--Iskovskikh单有理性构造。
英文摘要
We use the relative Abel--Jacobi construction of Cheltsov--Loginov--Orlov--Prokhorov to study unirational Fano threefolds. Our main result is a $50$-dimensional family of smooth unirational del Pezzo threefolds of degree one. We also construct explicit one-parameter families of terminal unirational sextic double solids and quartic threefolds of Picard rank one. Finally, we reinterpret the Roth--Iskovskikh unirationality construction for smooth double quadric threefolds in terms of a correspondence induced by the relative Abel--Jacobi map.
