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Geometry |
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Authors: B. Wang
Let $X$ be a compact K"ahler manifold. We first define the positivity of homology classes in $H_{2k}(X;mathbb Q)$.From the positivity, we extract complex analytic cycles. Precisely, we show if $tauin H_{2k}(X;mathbb Q)$ is positive, i.e. $tau $ is represented by a closed, strongly positive current, then there are a complex analytic cycle $V$ with positive rational coefficients and a positive current $S$ of bidimension $(k, k)$ such thatbegin{equation}tau=[T_V+S]end{equation}where $T_{bullet}$ denotes the current of integration over the chain $bullet$, and $[bullet]$ denotes the homologyclass represented by $bullet$.
Comments: 10 Pages.
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[v1] 2026-03-12 11:19:28
[v2] 2026-03-25 23:58:50
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