无复形的Kustin-Miller非投影
Kustin--Miller unprojection without complexes
摘要：
Gorenstein投影在双有理几何中起着关键的作用;典型的例子是d次的del Pezzo曲面到d-1次曲面的线性投影，但同一思想的变体提供了许多经典和现代的Fano 3-folds之间的双有理联系。逆运算是Kustin-Miller非投影定理（A. Kustin和M. Miller，Constructing big Gorenstein ideals from small ones，J. Algebra 85（1983）303- 322），其从“较不复杂”的Gorenstein环开始构造“较复杂”的Gorenstein环（将余维数增加1）。我们给出了一个干净的陈述和证明他们的定理，使用的对偶层的附加公式代替他们的复形和Buchsbaum-Eisenbud精确性准则。我们的方法是计划理论和工作没有任何提及的周围空间。因此，它们并不局限于当地的情况，并且很好地适应了概括。最后一节包含的例子，并简要讨论了应用分次环和双有理几何，激发本研究。
英文摘要：
Gorenstein projection plays a key role in birational geometry; the typical example is the linear projection of a del Pezzo surface of degree d to one of degree d-1, but variations on the same idea provide many of the classical and modern birational links between Fano 3-folds. The inverse operation is the Kustin--Miller unprojection theorem (A. Kustin and M. Miller, Constructing big Gorenstein ideals from small ones, J. Algebra 85 (1983) 303--322), which constructs "more complicated" Gorenstein rings starting from "less complicated" ones (increasing the codimension by 1). We give a clean statement and proof of their theorem, using the adjunction formula for the dualising sheaf in place of their complexes and Buchsbaum--Eisenbud exactness criterion. Our methods are scheme theoretic and work without any mention of the ambient space. They are thus not restricted to the local situation, and are well adapted to generalisations. The final section contains examples, and discusses briefly the applications to graded rings and birational geometry that motivate this study.
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