Talk:Hodge structure
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So what exactly is W_0, W_1, and W_2 in the example of curves? (the author is so close to making this explicit!) — Preceding unsigned comment added by 78.239.179.184 (talk) 16:28, 11 April 2012 (UTC)
To 99.241.86.114. Thanks for your formatting improvement and latex to html. I'll improve Japanese version as you've done.--Enyokoyama (talk) 10:16, 16 March 2013 (UTC)
Fix Formatting
[edit]Does anyone know how to fix the formatting on this page after the hodge diamond for the K3 surface?
Second definition of pure Hodge structure
[edit]In the second definition of pure Hodge structure, don't we need the condition that F^p H \oplus \overline{F^q H} = H for every p, q with p+q=n+1? If we only assume F^p H \cap \overline{F^q H} = 0, then the second definition is not equivalent to the first: e.g. take H_Z = Z, n=0, F^{-1} H = H, F^0 H = 0, then all H^{p,q} = 0, so H \neq \bigoplus_{p+q=n} H^{p,q}. 141.201.165.135 (talk) 12:11, 11 September 2013 (UTC)
Thanks!
[edit]This is a great article: it has the right level of generality, good examples, good writing. Thanks to the anon who wrote it. If there is some way to nominate technical articles to "good article" status, I would recommend doing so. Mvaintrob (talk) 18:51, 30 April 2016 (UTC)
Todo
[edit]- add Hirzebruch's generating function for computing hodge diamonds of complete intersections
- give explicit mixed hodge structure for a curve with points removed using log-de-Rham cohomology
- discuss monodromy for mixed hodge structures
- create mixed hodge module page — Preceding unsigned comment added by 97.122.75.155 (talk) 01:33, 3 July 2017 (UTC)
Splitting Pages
[edit]I think there should be a split creating a page for (pure) hodge structures and mixed hodge structures. This page seems a little cramped with both topics. Moreover, having a page dedicated to mixed hodge structures could include material on applications, such as cohomology of smooth affine varieties, singularity theory, and variations of mixed hodge structures. — Preceding unsigned comment added by 71.205.224.144 (talk) 23:28, 22 July 2017 (UTC)
- Support: primary because the article is already lengthy and also because mixed Hodge str is an important topic (as noted above). -- Taku (talk) 00:29, 23 July 2017 (UTC)
- I disagree on splitting mixed from pure Hodge structures. First, I don't see a reason to split: the article is definitely not too long. (If we really have to split, let's rather split off mixed Hodge modules and / or variations of Hodge structures). More importantly, mixed Hodge structures just rely so strongly on pure Hodge structures that a good article on mixed HS would repeat much of the article on pure HS. Jakob.scholbach (talk) 21:53, 23 July 2017 (UTC)
- By "length" I guess it's not just about the sheer number of bytes but the complexity of topics; i.e., there are many subtopics to the topic "mixed Hodge str". I'm positive that this is what the proposer meant by "This page seems a little cramped with both topics." I got exactly the same sense (hence my support). I don't have a background in this area but for example there is a book called "mixed Hodge structure", which suggests the topic deserves a page dedicated to it. But, since I lack expertise, I'm happy to let the decision to more knowledgeable editors. -- Taku (talk) 03:24, 24 July 2017 (UTC)
- Yes, mixed Hodge structures are definitely a noteworthy topic, but I highly doubt it works well to have two separate articles, one one pure, one on mixed Hodge structures.
- As I said, splitting off the topics on "higher dimensional Hodge structures" (i.e., mixed Hodge modules and variations of HS) seems a good move though, together with a brief exposition à la "Generalized notions" or the like in this article. Jakob.scholbach (talk) 07:51, 24 July 2017 (UTC)
- I disagree, we could just link the Hodge Structure page at the top of the Mixed Hodge Structure page. Then, we could have variations of (Mixed) Hodge structures on their designated page for Hodge Structures. Finally, there should be a Mixed Hodge Module page linking back to the rest of the hodge theory pages since this generalizes everything. In addition, the references section is kind of bloated. I want to add more example for computations of mixed hodge structures, but this page will start to blow up even more.
- You should see the scheduled material for the mixed hodge structure draft page. I put it in an HTML comment! This justifies having another page! — Preceding unsigned comment added by 73.14.173.69 (talk) 21:54, 10 August 2017 (UTC)
- By "length" I guess it's not just about the sheer number of bytes but the complexity of topics; i.e., there are many subtopics to the topic "mixed Hodge str". I'm positive that this is what the proposer meant by "This page seems a little cramped with both topics." I got exactly the same sense (hence my support). I don't have a background in this area but for example there is a book called "mixed Hodge structure", which suggests the topic deserves a page dedicated to it. But, since I lack expertise, I'm happy to let the decision to more knowledgeable editors. -- Taku (talk) 03:24, 24 July 2017 (UTC)
- I disagree on splitting mixed from pure Hodge structures. First, I don't see a reason to split: the article is definitely not too long. (If we really have to split, let's rather split off mixed Hodge modules and / or variations of Hodge structures). More importantly, mixed Hodge structures just rely so strongly on pure Hodge structures that a good article on mixed HS would repeat much of the article on pure HS. Jakob.scholbach (talk) 21:53, 23 July 2017 (UTC)
Examples of Mixed Hodge Structures
[edit]The Mixed Hodge Structure page should discuss the results in
http://archive.numdam.org/article/CM_1977__34_2_211_0.pdf
to give examples of computations of mixed hodge structures for a smooth affine hypersurface. In addition, it should discuss the material in
http://www.maths.ed.ac.uk/~aar/papers/steenbrink2.pdf
and the mixed hodge module page should discuss the results in
http://www.maths.ed.ac.uk/~aar/papers/steenbrink3.pdf http://www.mathunion.org/ICM/ICM1990.1/Main/icm1990.1.0569.0576.ocr.pdf https://core.ac.uk/download/pdf/82517402.pdf https://arxiv.org/pdf/1412.8499.pdf — Preceding unsigned comment added by 71.196.153.244 (talk) 05:30, 30 October 2019 (UTC)
with => explicit examples included <= — Preceding unsigned comment added by 161.98.8.4 (talk) 21:53, 9 August 2017 (UTC)
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