Kuznetsov’s homological projective duality (HPD) theory [K4] is one of the most active and powerful recent developments in the homological study of algebraic geometry. The fundamental theorem of HPD systematically compares derived categories of dual linear sections of a pair of HP-dual varieties $(X,X^{\natural})$.In this paper we generalize the fundamental theorem of HPD beyond linear sections. More precisely, we show that for any two pairs of HP-duals $(X,X^{\natural})$ and $(T,T^{\natural})$ which intersect properly, there exist semiorthogonal decompositions of the derived categories $D(X \cap T)$ and $D(X^{\natural} \cap T^{\natural})$ into primitive and ambient parts, and that there is an equivalence of primitive parts $^\mathrm {prim} D(X \cap T) \simeq D(X^{\natural} \cap T^{\natural})^{\mathrm prim}$.

中文翻译：

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分类Plücker公式和同调射影对偶

库兹涅佐夫的同构射影对偶性（HPD）理论[K4]是代数几何同构研究中最活跃，最有力的发展之一。HPD基本定理系统地比较了一对HP对偶变种$（X，X ^ {\ natural}）$的双重线性部分的派生类别。在本文中，我们推广了HPD基本定理，超越了线性部分。更准确地说，我们表明，对于正确相交的任何两对HP对偶$（X，X ^ {\ natural}）$和$（T，T ^ {\ natural}）$，存在派生子的半正交分解将$ D（X \ cap T）$和$ D（X ^ {\ natural} \ cap T ^ {\ natural}）$分为原始部分和周围部分，并且等价的原始部分$ ^ \ mathrm { prim} D（X \ cap T）\ simeq D（X ^ {\ natural} \ cap T ^ {\ natural}）^ {\ mathrm prim} $。