4,284 reputation
834
bio website nullteilerfrei.de
location Germany
age 29
visits member for 3 years, 6 months
seen 9 mins ago

I'm a PhD student with research interests in Algebraic Geometry, Algebraic Complexity Theory and Geometric Invariant Theory.


Aug
22
revised Ideal defining the nilpotent cone of $\mathfrak{gl}_n(k)$
deleted 16 characters in body
Aug
22
answered Ideal defining the nilpotent cone of $\mathfrak{gl}_n(k)$
Aug
21
answered Clarification of definition of category
Aug
17
comment Time complexity of a modulo operation
@ShreevatsaR: You're right. Absolutely 100% right. I frankly don't expect any upvotes. But since the question was unanswered and doesn't seem to get that much attention, I thought a literature reference is better than nothing =D.
Aug
17
comment Time complexity of a modulo operation
@ShreevatsaR: No offense, but that would be quite time-consuming. In addition, it feels rather pointless (to me personally) when there is a reference that does explain it. I would suggest a library.
Aug
15
comment Test for equivalence of algebraic expressions
To be honest, that sounds very difficult to me. However, computer algebra systems can do this to a certain degree. I am reasonably sure I would suggest Buchberger's book on computer algebra, had I read it. Seriously, I do not know how this is done at all, but I am quite sure that existing computer algebra systems implement algorithms that are well-known and covered in graduate textbooks. Unless someone more knowledgeable posts here, I suggest you dig through some of them.
Aug
15
comment What does it mean for the coordinate ring of an affine variety to be graded?
First of all, thanks for your answer. However, it's not quite what I was looking for (yet): In fact, what you said is my motivation to ask the question. Having $k^\times$ act on $X$ gives me a $\mathbb Z$-grading indeed, but this grading does not have to come from a polynomial ring, or are you saying that it does? Does every affine $k^\times$ variety admit a $k^\times$-morphism that is an immersion into some $\mathbb A^n$?
Aug
15
comment Math-related open source software to contribute to
I just realized, also @lhf, Maybe this should be community wiki?
Aug
15
comment Math-related open source software to contribute to
You might find this blog post informative.
Aug
15
asked What does it mean for the coordinate ring of an affine variety to be graded?
Aug
15
revised A question of sheaf
Little bit of LaTeX cosmetics, little bit of typos.
Aug
2
comment Test for equivalence of algebraic expressions
Could you be more precise about what kind of function you would like to test? When you say algebraic expression, do you mean a polynomial? In this case, you might be interested in the Schwarz-Zippel-Lemma which yields a very easy randomized algorithm: Simply evaluate your polynomials at sufficiently many random points.
Jul
30
comment Ramification divisor and Hurwitz formula of higher dimensionanl vaireities
Yea I ment that for the case where $f$ is smooth. If you read a bit further in that Chapter of Liu's book, he has Theorem 4.9 (the numbering is a bit weird, that's the 9th theorem in 6.4) which is $\omega_X\cong \omega_{X/Y}\otimes_{\mathcal O_X} f^\ast \omega_Y$ for $f$ a quasi-projective locally complete intersection. Better than that, I am afraid I cannot offer.
Jul
30
comment Ramification divisor and Hurwitz formula of higher dimensionanl vaireities
You're completely right. I think what you're looking for is in Qing Liu's book, see my edit.
Jul
30
revised Ramification divisor and Hurwitz formula of higher dimensionanl vaireities
added 953 characters in body
Jul
29
answered intuitive interpretation of dimension of an affine variety
Jul
29
answered Ramification divisor and Hurwitz formula of higher dimensionanl vaireities
Jul
15
answered Polynomials and the inverse matrix
Jul
5
comment Projection is an open map
@WishingFish: See my edit. Hope this helps!
Jul
5
revised Projection is an open map
added 747 characters in body