Explicit Serre duality on complex spaces

• In this paper we use recently developed calculus of residue currentstogether with integral formulas to give a new explicit analytic realization, as wellas 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 concretefine sheaves $A^{n,q}_X$ of certain currents on X of bidegree (n,q), such that the corresponding Dolbeault complex becomes, in a certain sense, a dualizing complex. Inparticular, if X is Cohen-Macaulay (e.g., Gorenstein or a complete intersection)then this Dolbeault complex becomes an explicit fine resolution of the Grothendieck dualizing sheaf.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Publication and Content Type

art (subject category)

ref (subject category)