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Zenodo
2026
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| Accesso online: | https://doi.org/10.5281/zenodo.18897774 |
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| _version_ | 1866901774985592832 |
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| author | Washburn, Jonathan |
| author_facet | Washburn, Jonathan |
| contents | <p>This four-paper series develops a machine that converts smooth closed uniformly positive strongly positive (p,p)-forms on a smooth complex projective manifold into algebraic cycles representing their cohomology classes. Paper I constructs holomorphic complete-intersection pieces at the Bergman scale with quantitative tangent, mass, and face-trace control. Paper II organizes those pieces into coherent assembly packets via Caratheodory decomposition, Lipschitz-stable direction labeling, and a vertex-prefix face-balancing mechanism that yields a global boundary flat-norm bound. Paper III converts such packets into closed integral cycles in an exact prescribed homology class with vanishing calibration defect, using a period-first rounding principle that separates cohomological locking from geometric closure. Paper IV passes to a calibrated holomorphic limit via Federer--Fleming compactness and identifies the result as an algebraic cycle by the Harvey--Lawson/King structure theorem and Chow/GAGA. A signed decomposition then extends the conclusion from cone-positive classes to all rational (p,p)-Hodge classes, for all 1 <= p < n</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18897774 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Calibrated discretization and algebraic realization of rational (p,p)-classes Washburn, Jonathan <p>This four-paper series develops a machine that converts smooth closed uniformly positive strongly positive (p,p)-forms on a smooth complex projective manifold into algebraic cycles representing their cohomology classes. Paper I constructs holomorphic complete-intersection pieces at the Bergman scale with quantitative tangent, mass, and face-trace control. Paper II organizes those pieces into coherent assembly packets via Caratheodory decomposition, Lipschitz-stable direction labeling, and a vertex-prefix face-balancing mechanism that yields a global boundary flat-norm bound. Paper III converts such packets into closed integral cycles in an exact prescribed homology class with vanishing calibration defect, using a period-first rounding principle that separates cohomological locking from geometric closure. Paper IV passes to a calibrated holomorphic limit via Federer--Fleming compactness and identifies the result as an algebraic cycle by the Harvey--Lawson/King structure theorem and Chow/GAGA. A signed decomposition then extends the conclusion from cone-positive classes to all rational (p,p)-Hodge classes, for all 1 <= p < n</p> |
| title | Calibrated discretization and algebraic realization of rational (p,p)-classes |
| url | https://doi.org/10.5281/zenodo.18897774 |