User talk:David Lehavi: Difference between revisions
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2) The sentence: "Thus, the moduli of 2g + 2 distinct points on \mathbb{P}^1 up to projective transformations is a finite quotient of the space of distinct 2g − 1 on \mathbb{P}^1\setminus\{0,1,\infty\}" does not make sense to me. You are talking about the moduli space of sets of 2g-1 distinct points, or what? | 2) The sentence: "Thus, the moduli of 2g + 2 distinct points on \mathbb{P}^1 up to projective transformations is a finite quotient of the space of distinct 2g − 1 on \mathbb{P}^1\setminus\{0,1,\infty\}" does not make sense to me. You are talking about the moduli space of sets of 2g-1 distinct points, or what? | ||
3) You talk about "the moduli of 2g + 2 distinct points on \mathbb{P}^1". Do you mean the moduli space | 3) You talk about "the moduli of 2g + 2 distinct points on \mathbb{P}^1". Do you mean the moduli space which parameterise sets of 2g+2 distinct points on ...." Sorry, I don't know much about moduli spaces, so I didn't know if your terminology was standard, or what it means. | ||
4) The references need to be expanded, with full Author, Title, Publisher references being given. | 4) The references need to be expanded, with full Author, Title, Publisher references being given. | ||
I think that all these articles are going to need an introduction written for non-experts, i.e. for people who do not have a graduate understanding of algebraic geometry, or who work in a completely different field of mathematics. The introduction wouldn't be designed to explain the algebraic geometry that you have written about, which is too technical to explain to someone who doesn't already understand it. Rather, the introduction should just give a quick non-expert introduction to what a hyperelliptic curve is, for example, without describing any of its more complicated properties. For example it might say that a hyperelliptic curve is a plane curve (perhaps say a little more explicitly what a plane curve is, in plain language) which satisfies an equation of the form.... State how hyperelliptic curves are related to elliptic curves. Say something about why hyperelliptic curves are important in mathematics (I don't think it is enough to state that they have applications in cryptography, I think the article should state why they are important in algebraic geometry, e.g. because they have a particularly simple model which can be written down, etc). What do you think? [[User:William Hart|William Hart]] 07:26, 1 March 2007 (CST) | I think that all these articles are going to need an introduction written for non-experts, i.e. for people who do not have a graduate understanding of algebraic geometry, or who work in a completely different field of mathematics. The introduction wouldn't be designed to explain the algebraic geometry that you have written about, which is too technical to explain to someone who doesn't already understand it. Rather, the introduction should just give a quick non-expert introduction to what a hyperelliptic curve is, for example, without describing any of its more complicated properties. For example it might say that a hyperelliptic curve is a plane curve (perhaps say a little more explicitly what a plane curve is, in plain language) which satisfies an equation of the form.... State how hyperelliptic curves are related to elliptic curves. Say something about why hyperelliptic curves are important in mathematics (I don't think it is enough to state that they have applications in cryptography, I think the article should state why they are important in algebraic geometry, e.g. because they have a particularly simple model which can be written down, etc). What do you think? [[User:William Hart|William Hart]] 07:26, 1 March 2007 (CST) | ||
Revision as of 07:27, 1 March 2007
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Feedback
Hi David,
Thanks for your message and welcome to Citizendium, I'm happy you want to contribute here. I'm flattered you chose me to ask for feedback.
Broadly speaking I think I would advise three things....
- Try to scale the article so that it has bits that will matter to all of the following three groups: people with very little background knowledge; people with some knowledge and technical skills but who are not virtuosos; and highly technical, knowledgeable people who need a serious reference up to the highest level. You don't have to cater for them in order, just make sure the article is structured so that technical bits are skippable for those who don't need/understand them.
- The intro has to be the most universally accessible part of the whole article. You can and should include the key technical definition but cater as much as possible to those with the minimum level of knowledge. Don't dumb down---be open and honest with your reader about when you are giving them a friendly approximation rather than the real thing, and always provide the precise material to go with it.
- Write prose that you personally find attractive and friendly, as well as correct, and where you can provide graphics to help ease the visualisation of ideas.
Hope that helps! Keep in touch, —Joseph Rushton Wakeling 18:32, 19 February 2007 (CST)
Hi David,
I corrected some spelling and grammatical errors in the article on hyperelliptic curves, which reads well overall. However there are four problems remaining which I have not fixed yet. You are probably in a better position to fix these than I am:
1) In the sentence: "If we count each set S together with its complementary set in the set of Weierstrass points (and then divide by 2) then the combinatorial description above tells us that any partition of the set of Weierstrass points into two sets such that the difference between the cardinalities is divisible by 4 induces a theta characteristic. We count \frac{1}{2}\sum_{4|2g+2-2k}\mbox{binom}(2g+2,k)." I do not know what the sum is counting. Is it points, Weierstrass points, or theta characteristics. The sentence which I changed to say "We count..." should probably say "Performing this calculation, we count .... Weierstrass points." or something like that. But I didn't know what it was supposed to say.
2) The sentence: "Thus, the moduli of 2g + 2 distinct points on \mathbb{P}^1 up to projective transformations is a finite quotient of the space of distinct 2g − 1 on \mathbb{P}^1\setminus\{0,1,\infty\}" does not make sense to me. You are talking about the moduli space of sets of 2g-1 distinct points, or what?
3) You talk about "the moduli of 2g + 2 distinct points on \mathbb{P}^1". Do you mean the moduli space which parameterise sets of 2g+2 distinct points on ...." Sorry, I don't know much about moduli spaces, so I didn't know if your terminology was standard, or what it means.
4) The references need to be expanded, with full Author, Title, Publisher references being given.
I think that all these articles are going to need an introduction written for non-experts, i.e. for people who do not have a graduate understanding of algebraic geometry, or who work in a completely different field of mathematics. The introduction wouldn't be designed to explain the algebraic geometry that you have written about, which is too technical to explain to someone who doesn't already understand it. Rather, the introduction should just give a quick non-expert introduction to what a hyperelliptic curve is, for example, without describing any of its more complicated properties. For example it might say that a hyperelliptic curve is a plane curve (perhaps say a little more explicitly what a plane curve is, in plain language) which satisfies an equation of the form.... State how hyperelliptic curves are related to elliptic curves. Say something about why hyperelliptic curves are important in mathematics (I don't think it is enough to state that they have applications in cryptography, I think the article should state why they are important in algebraic geometry, e.g. because they have a particularly simple model which can be written down, etc). What do you think? William Hart 07:26, 1 March 2007 (CST)