Source / pinned edition
Lefschetz (1,1)-theorem (1924), proved here via the Kodaira-Spencer (1953) exponential-sequence argument, as reproduced in Deligne's official CMI Hodge conjecture description
Source of package lefschetz.degree_two_1924 · https://www.claymath.org/wp-content/uploads/2022/06/hodge.pdf#remark-iii
- work
- urn:doctrine:math:lefschetz-1-1-1924#LEFSCHETZ_KODAIRA_SPENCER_EXPOSITION
- number
- https://www.claymath.org/wp-content/uploads/2022/06/hodge.pdf#remark-iii
- kind
- urn:doctrine:math:lefschetz-1-1-1924#treatise
LEFSCHETZ_EXPOSITION_EDITION
- edition
- urn:doctrine:math:lefschetz-1-1-1924#LEFSCHETZ_EXPOSITION_EDITION
- language
- en
- officiality
- unofficial
- materialisation
- PINNED_UNOFFICIAL_COPY
- life cycle
- —
Publications
| URI | Type | documentHash | Retrieved |
|---|---|---|---|
| https://www.claymath.org/wp-content/uploads/2022/06/hodge.pdf | text/plain; charset=utf-8 | sha256:d631f79365fbc569ed92e83e02958b6735188f52072651f93444e7e6428efc0a | 2026-09-17T00:00:00Z |
Fragments — 1
remark-iii · lemma · referenced by: 5
en · official · sha256:97e5081e7f24ba889b78ff4d737db1b771947d1e8b99cbc304a0d905e2f290f7
(iii) A particular case of (ii) is that the integral linear combinations of classes of divisors (= codimension 1 cycles) are simply the first Chern classes of line bundles. If Z+ - Z- is the divisor of a meromorphic section of L, c1(L) = cl(Z+) - cl(Z-). This is the starting point of the proof given by Kodaira and Spencer [7] of the Hodge conjecture for H^2: a class c in H^2(X,Z) of type (1,1) has image 0 in the quotient H^{0,2} = H^2(X,O) of H^2(X,C), and the long exact sequence of cohomology defined by the exponential exact sequence 0 -> Z -> O -[exp(2 pi i .)]-> O* -> 0 shows that c is the first Chern class of a line bundle.Referencing norms: LefschetzDegree2Direct, LefschetzProof, LefschetzSource, lefschetz-proves-degree2, lefschetz_degree2_established_for
The hash beside the text is the sha256 of its exact bytes. It is the check that the text shown matches the one pinned in the package: a divergence fails the oracle’s static analysis.