Geodesic
The Sheaf
Journal of Singularities, Tome 18 (2018), pp. 50-83

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We introduce, in a reduced complex space, a "new coherent sub-sheaf" of the sheaf \omega_X^\bullet which has the "universal pull-back property" for any holomorphic map, and which is, in general, bigger than the usual sheaf of holomorphic differential forms (\Omega_X^\bullet)/torsion. We show that the meromorphic differential forms which are sections of this sheaf satisfy integral dependence equations over the symmetric algebra of the sheaf (\Omega_X^\bullet)/torsion. This sheaf \alpha_X^\bullet is closely related to the normalized Nash transform. We also show that these q-meromorphic differential forms are locally square-integrable on any q-dimensional cycle in X and that the corresponding functions obtained by integration on an analytic family of q-cycles are locally bounded and continuous on the complement of a closed analytic subset.
DOI : 10.5427/jsing.2018.18e
Classification : 32C15, 32C30, 32Sxx, 32S45 
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     author = {Daniel Barlet},
     title = {The {Sheaf}},
     journal = {Journal of Singularities},
     pages = {50--83},
     publisher = {mathdoc},
     volume = {18},
     year = {2018},
     doi = {10.5427/jsing.2018.18e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.18e/}
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Daniel Barlet. The Sheaf. Journal of Singularities, Tome 18 (2018), pp. 50-83. doi: 10.5427/jsing.2018.18e

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