Explicit Serre duality on complex spaces

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• 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 class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816313391&_mathId=si1.gif&_user=111111111&_pii=S0001870816313391&_rdoc=1&_issn=00018708&md5=bdfae97446b7f0f7cc461be3d1ef4297">class="imgLazyJSB inlineImage" height="17" width="36" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0001870816313391-si1.gif">class="mathContainer hidden">class="mathCode">${\mathcal{B}}_X^{n,q}$ of currents on X   of bidegree class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816313391&_mathId=si2.gif&_user=111111111&_pii=S0001870816313391&_rdoc=1&_issn=00018708&md5=d07dc79eec352cd60992340f2cb366da" title="Click to view the MathML source">(n,q)class="mathContainer hidden">class="mathCode">$(n,q)$, such that the Dolbeault complex class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816313391&_mathId=si3.gif&_user=111111111&_pii=S0001870816313391&_rdoc=1&_issn=00018708&md5=5ff5f1a1fc2dc5f2812e0ea646c10d09">class="imgLazyJSB inlineImage" height="19" width="66" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0001870816313391-si3.gif">class="mathContainer hidden">class="mathCode">$({\mathcal{B}}_X^{n,•},\overline{\partial })$ becomes, in a certain sense, a dualizing complex. In particular, if X   is Cohen–Macaulay then class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870816313391&_mathId=si3.gif&_user=111111111&_pii=S0001870816313391&_rdoc=1&_issn=00018708&md5=5ff5f1a1fc2dc5f2812e0ea646c10d09">class="imgLazyJSB inlineImage" height="19" width="66" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0001870816313391-si3.gif">class="mathContainer hidden">class="mathCode">$({\mathcal{B}}_X^{n,•},\overline{\partial })$ is an explicit fine resolution of the Grothendieck dualizing sheaf.