Abstract
Let X be a projective algebraic variety over ℂ of dimension d, reduced and irreducible. In this paper we propose a definition for differential forms w of degree d on X to be holomorphic at an arbitrary point of X (which may be a singular point). It will be shown that the holomorphic d-forms define a sheaf ωX, which coincides with the usual sheaf of holomorphic d-forms ωX in case X has no singularities. Moreover, ωX is isomorphic to the canonical sheaf
of Grothendieck [5]:
, (if X is a closed subvariety of ℙn). Thus in the Serre duality theorem for projective varieties with singularities
may be replaced by ωX.
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Kunz, E. Holomorphe Differentialformen auf algebraischen Varietäten mit Singularitäten I. Manuscripta Math 15, 91–108 (1975). https://doi.org/10.1007/BF01168881
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DOI: https://doi.org/10.1007/BF01168881