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May
6
answered Is a pattern proof?
Apr
22
comment Correspondence between morphism and ring of regular functions
I find it helpful to think of a regular map from affine $X \to Y \subset A^n$ as $n$ polynomials $f = (f_1, \ldots, f_n)$ , such that $f(X) \subset Y$, Hartshorne proves these are equivalent later in the chapter.
Apr
18
asked “Cohomology classes correspond to homotopy classes of maps to Eilenberg Maclane spaces” and cup product?
Apr
18
accepted What kind of information is available in a Fourier series expansion of an analytic function that is not (readily) available in a Taylor series?
Apr
18
asked What kind of information is available in a Fourier series expansion of an analytic function that is not (readily) available in a Taylor series?
Apr
18
asked How to distinguish the tautological line bundle and the trivial line bundle on $P^n$?
Apr
14
accepted Given the set of all polygons with m sides and perimeter 1, why is there an element with maximal area?
Apr
14
comment Given the set of all polygons with m sides and perimeter 1, why is there an element with maximal area?
This makes sense, but what is a 2D cross product?
Apr
14
asked Given the set of all polygons with m sides and perimeter 1, why is there an element with maximal area?
Apr
9
asked When is a wedge decomposible?
Apr
1
asked Surjective morphism of varieties with finite fibers but not “finite”
Mar
28
accepted Based on the Andreotti-Frankel theorem, what is the CW complex homotopy equivalent to $x^2 + y^2 - 1$?
Mar
28
asked Based on the Andreotti-Frankel theorem, what is the CW complex homotopy equivalent to $x^2 + y^2 - 1$?
Mar
13
comment Problem 2.26 in Fulton's Algebraic Curves: redundant hypothesis?
2.26 I think...
Mar
13
comment Problem 2.26 in Fulton's Algebraic Curves: redundant hypothesis?
Because the hypothesis in the text is that S is a DVR, and later on I want to use this result to classify DVRs over PIDS contained in the residue field. Maybe there is no problem, I just wanted to be sure I guess.
Mar
13
revised Problem 2.26 in Fulton's Algebraic Curves: redundant hypothesis?
edited body
Mar
13
asked Problem 2.26 in Fulton's Algebraic Curves: redundant hypothesis?
Feb
22
comment When is a morphism of $k$-ringed spaces the morphism induced by pullbacks?
Oh I see. That makes sense. Thanks for your patience - these ideas are pretty new to me.
Feb
22
comment When is a morphism of $k$-ringed spaces the morphism induced by pullbacks?
Thanks. In response to your original answer: In the smooth or complex case, how does the definition insure that the residue fields are the real numbers or complex numbers respectively? Surely I can have locally R-ringed spaces where some residue fields are C (such as $Spec R[x]$ at the prime $(x^2 + 1)$)...
Feb
22
comment The series $\sum_{n=1}^\infty\frac1n$ diverges
@hunter But $>$ in general becomes $\geq$ in a limit. Else $1/n > 0$ implies $0 = lim 1/n > 0$