Jesko Hüttenhain
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 Jun 11 answered When does the regularity of $A$ implies the regularity of $A[w]$? Jun 9 revised Better understanding regular functions on a Projective variety added 14 characters in body Jun 5 answered Isomorphic projective subvarieties, non-isomorphic rings Jun 5 revised Blow-up of pair of intersecting lines deleted 47 characters in body Jun 5 answered Blow-up of pair of intersecting lines Jun 4 comment A categorical approach to algebraic geometry I haven't read it, but you might have a look at Categories and Sheaves by Masaki Kashiwara and Pierre Schapira. It seems to contain lots of the stuff you want. Jun 2 awarded Yearling May 21 revised Zeroes of prime polynomials in the algebraic torus (A Hilbert's Nullstellensatz for Laurent polynomials?) added 213 characters in body May 21 comment Zeroes of prime polynomials in the algebraic torus (A Hilbert's Nullstellensatz for Laurent polynomials?) You are, of course, completely correct. Regarding your second thing, I missed the "different" ... so yea, you are right about that, too. May 21 answered Zeroes of prime polynomials in the algebraic torus (A Hilbert's Nullstellensatz for Laurent polynomials?) May 20 comment Can someone illustrate the definition of manifold with a simple example? The most classical example would be the sphere in $\mathbb R^3$. For any point $x$, you can pick the point opposite to it $y$ and use the stereographic projection map to identify $M\setminus\{y\}$ with $\mathbb R^2$. May 19 awarded Enlightened May 19 awarded Nice Answer May 19 comment Dimension of affine part equals to the dimension of the variety The dimension of $\mathbb P^n$ is not equal to the Krull dimension of its projective coordinate ring $k[x_0,\ldots,x_n]$, which is $n+1$. That's because $\mathbb P^n$ is not an affine variety. The problem with your question is that it is ill-posed: What is your definition of the dimension of $\mathbb P^n$? May 18 comment Inclusion of Tori induces surjection of character groups? This is true, but I have too little time for anything but a reference right now: Tauvel & Yu, Lie algebras and algebraic groups, 22.5.4 (iii) is a slightly more general statement for diagonalizable algebraic groups. Any torus is diagonalizable, of course. May 12 comment Inclusionwise maximal linear subvarieties of a projective variety @DanielMcLaury: Interesting, I didn't see that angle. If I am not somehow mistaken, this is the image of a projective morphism, so it should be closed. Any flaws in that argument? May 12 asked Inclusionwise maximal linear subvarieties of a projective variety May 10 accepted Is every codimension one subvariety of a projective variety a set-theoretic complete intersection? May 10 revised Is every codimension one subvariety of a projective variety a set-theoretic complete intersection? added 639 characters in body; edited tags May 10 asked Is every codimension one subvariety of a projective variety a set-theoretic complete intersection?