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Jun
11
awarded  Nice Answer
Jun
1
comment When do the Nakano identities hold?
... there's some non-trivial work going on in the background that makes the argument go through, here we need to do some work to show that some suitable taylor series converges in remark 4.2.5. I'm sorry this isn't more useful, but if you're still interested in a couple of weeks, check back and I'll see if I can remember what I thought the answer was and post it.
Jun
1
comment When do the Nakano identities hold?
@Dtseng I think I found part of the problem, I was going to post an answer once exams finish, and probably e-mail Ross about it too. The fact that not all smooth frames are holomorphic is what was causing some of the problems originally. Huybrechts refers to "Remark 4.2.5" in his book for how we can take a holomorphic frame. This is where we need the connection to be the Chern connection, since properties of the matrix A are used with the content of this remark. I don't really fully understand it, and as with much of Huybrechts...
May
13
revised What are some examples of principal, proper ideals that have height at least $2$?
edited tags
May
13
revised What are some examples of principal, proper ideals that have height at least $2$?
edited body
May
12
answered The Dimension Sequence of a Ring
May
11
awarded  Proofreader
May
11
reviewed Approve Area of a triangle from some of its parts
May
9
reviewed Approve Using the Newton-Quotient
May
9
reviewed Close Diffeomorphism ( differential geometry)
May
9
reviewed Close Solve the integral $\int \frac{\sinh\left(x\right)-2}{2\sinh\left(x\right)+\cosh\left(x\right)}dx$
May
9
reviewed Leave Open What is the maximum number of $15 cm\times 15 cm$-square I can cut from a diameter $50 cm$- circle?
May
9
reviewed Close Prove or disprove the following statements
May
9
reviewed Leave Open Background required to understand the mathematical definition of knots and their transformations
May
9
asked When do the Nakano identities hold?
May
7
answered De Rham-Weil theorem
May
6
reviewed Looks OK How to calculate difference between two points in some values?
May
5
comment Sheafification, stalks and quotient
@user198182 You're welcome. I would say that both things are very straightforward to prove and could reasonably be said to be obvious. I try and avoid saying it where possible since something being obvious is always relative. But I'm glad it was helpful!
May
5
answered Sheafification, stalks and quotient
May
3
comment Localizing and taking degree zero commutes with tensor product
I don't think this is true in general when the degree of $f$ is not $1$, since then we need not have $(M_f\otimes_{S_f} N_f)_{(0)}\cong M_{(f)}\otimes_{S_{(f)}}N_{(f)}$. For example, if $f = X_1^2$, then $m\otimes n / X_1^2$ is in the former but not necessarily in the latter. Perhaps I am mistaken but I have seen several sources claim that this is an isomorphism specifically for $deg(f) = 1$.