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Yesterday my first work in mathematics was sent to a publisher, and of course I'm interested in its usefulness. But I know, that sometimes it is hard to get a paper, it is not available for free. I hope my paper will not be of that kind. I hope it will be simple to find it and to read it, I hope a few hundred people will read it. Therefore I have this question. When do mathematicians usually lose their right to share their papers on the internet, why some of them doesn't like to do this and which ways are there to overcome these "sharing difficulties"?

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This should be Comunity Wiki I guess. My answer: arXiv! –  rpotrie Oct 14 '10 at 14:19
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I think that in most cases, not sharing work on the internet is more a reflection of a mathematician's personal taste (so to speak) --- i.e. whether they can be bothered or think it's important to do this --- rather than of copyright issues (regardless of what the actual legal status of their ownership over their papers is). The one common exception that I'm aware of in this regard is the case of books: these represent a somewhat more substantial investment by the publisher than any one paper, and so I think authors are less likely to keep electronic copies of their books ... –  Emerton Oct 14 '10 at 14:23
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... available online after the book is published (unless they have a publishing contract which explicitly allows them to distribute the book electronically even after it is published). –  Emerton Oct 14 '10 at 14:24
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Surely you signed a copyright agreement that lays out exactly what rights you have for sharing your paper? Unrelatedly, three small language notes: "loose" and "lose" are different, as are "its" and "it's." Also, the contraction "I've" can't be used when "have" is the main verb, only when it's a helper verb ("I've got problems," but "I have problems"). –  JBL Oct 14 '10 at 14:30
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@Emerton: publishers are surprisingly willing to let authors make their books available online. As recently as five years ago, it was a bit of a hard sale, though a determined author could make it happen. These days, it's a lot more commonplace: e.g., I was just looking this morning at this one algo.inria.fr/flajolet/Publications/books.html which came out in 2009. –  Thierry Zell Oct 14 '10 at 17:38
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Read any contract you sign carefully, otherwise you may lose rights you wanted to keep. In 2000, CRC Press sued Eric Weisstein because he posted free updates to the web of a mathematics book he had written and published with them.

Usually non-commercial publishers like the AMS allow you to keep any rights you want, while commercial publishers often try to get the rights for themselves (but will usually allow you to keep them if you make a fuss).

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Some journals are public access. Some journals make articles publicly available after some time period, for example a year. Others are complete paywalls.

There is a distinction between the document you submit and the edited document which is published; your freedom to distribute the edited document may be more limited, although you will typically be able to share on an individual basis with colleagues.

Also there is arxiv. I would bet that you would be allowed to keep your preprint on arxiv as long as it is untouched by an editor of a journal, but I'm not positive about this and I would like to know more myself.

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When you submit to the arXiv, you grant them a non-revokable license to offer your article for download. This is very convenient, as now it is no longer within your own rights to sign a copyright agreement that would require you to stop the arXiv from publishing your paper. In practice, publishers seem to accept that, i.e. the copyright assignment typically contains a clause that allows you to make the paper available online. Sometimes, they don't allow you to use the changes made by copy-editors, and sometimes they require the preprint to mention that it differs from the published version. –  Arend Bayer Oct 17 '10 at 14:03
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After your paper is accepted, you should politely ask the publisher for a version of the copyright form that either a) places the paper in the public domain or b) allows you to retain copyright. In my experience, a) sometimes works and b) always works.

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Fwiw the first option is much much better than the latter. The problem is that since copyright terms are now perpetual (i.e. will be expanded every time they're about to expire) if you retain copyright then when you die it will be impossible for anyone to ever obtain the rights to reprint it. –  Noah Snyder Oct 14 '10 at 18:12
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@Noah - I very much agree. However not all publishers (or perhaps their author-facing-editors) understand that a) is better for them than b) is. I have been told by a representative of Commentarii that placing work in the public domain does not protect the author's rights. The representative at Duke simply refused to discuss the issue, saying that the lawyers would not permit it. Those are the only negative experiences I can remember right now -- anyway, in those cases I just gave up and went with option b). –  Sam Nead Oct 14 '10 at 22:12
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I have, several times, rewritten the form I was sent; I then send the journal a copy of the new form and ask if that would be ok. –  Sam Nead Oct 14 '10 at 22:17
    
@Noah and Sam: Perhaps you could ask to reduce the copyright term of your paper to something more reasonable, like 28 years? At least this is the case with AMS: ams.org/notices/200403/commentary.pdf –  Dmitri Pavlov Oct 15 '10 at 14:55
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