The asymptotics of the holomorphic torsion forms

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• 作者：Martin Puchol ^{martin.puchol@imj-prg.fr" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Comptes Rendus Mathematique
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：354
• 期：3
• 页码：301-306
• 全文大小：286 K

文摘

In this note, we use the theory of Toeplitz operators to give an asymptotic formula for the holomorphic analytic torsion forms associated with a family of holomorphic vector bundles that are the direct image of 246&_mathId=si1.gif&_user=111111111&_pii=S1631073X15003246&_rdoc=1&_issn=1631073X&md5=343e139d5ced25af53405ca2f94d6eff" title="Click to view the MathML source">L^⊗p$L^{\otimes p}$, where L is a line bundle. To obtain the asymptotics, we make a positivity assumption along the fibers on L. This result is the family version of the results of Bismut and Vasserot on the holomorphic torsion.