Explicit Serre duality on complex spaces

详细信息    查看全文

• 作者：Jean Ruppenthal^a ; ¹ ; ^{ruppenthal@uni-wuppertal.de" class="auth_mail" title="E-mail the corresponding author} ; Hå ; kan Samuelsson Kalm^b ; ² ; ^{hasam@chalmers.se" class="auth_mail" title="E-mail the corresponding author} ; Elizabeth Wulcan^b ; ² ; ^{wulcan@chalmers.se" class="auth_mail" title="E-mail the corresponding author}
• 关键词：32A26 ; 32A27 ; 32B15 ; 32C30
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：1320-1355
• 全文大小：661 K

文摘

In this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization, as well as a new analytic proof, of Serre duality on any reduced pure n-dimensional paracompact complex space X  . At the core of the paper is the introduction of certain fine sheaves ${\mathcal{B}}_X^{n,q}$ of currents on X   of bidegree (n,q)$(n,q)$, such that the Dolbeault complex $({\mathcal{B}}_X^{n,•},\overline{\partial })$ becomes, in a certain sense, a dualizing complex. In particular, if X   is Cohen–Macaulay then $({\mathcal{B}}_X^{n,•},\overline{\partial })$ is an explicit fine resolution of the Grothendieck dualizing sheaf.