Homological projective duality for determinantal varieties

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• 作者：Marcello Bernardara^a ; ^{marcello.bernardara@math.univ-toulouse.fr" class="auth_mail" title="E-mail the corresponding author} ; Michele Bolognesi^b ; ^{michele.bolognesi@umontpellier.fr" class="auth_mail" title="E-mail the corresponding author} ; Daniele Faenzi^c ; ¹ ; ^{daniele.faenzi@u-bourgogne.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Derived category ; Semi-orthogonal decompositions ; Projective varieties ; Determinantal varieties ; Homological projective duality ; Rationality questions
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：25 June 2016
• 年：2016
• 卷：296
• 期：Complete
• 页码：181-209
• 全文大小：562 K

文摘

In this paper we prove Homological Projective Duality for categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a m×n$m\times n$ matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi–Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.