Reputation
Next tag badge:
135/100 score
19/20 answers
Badges
4 90 195
Newest
 Enlightened
Impact
~536k people reached

23h
revised Hodge Theory, intuition?
Added formula for Poincaré duality
1d
answered Hodge Theory, intuition?
1d
comment Is “Categories and Sheaves” a good followup to Aluffi's “Algebra: Chapter 0”?
@Pece: nice slogan, that!
1d
comment Is “Categories and Sheaves” a good followup to Aluffi's “Algebra: Chapter 0”?
Dear Saal, it makes me very happy that I could be of help. And, yes, algebraic topology is a wonderful subject. It is there that I first saw the power of functorial thinking: applying suitable functors like $\pi_1$ or $H_i$ solves some problems so easily that one has the feeling one is cheating. But, hey, in love and math all is fair :-)
1d
comment Is “Categories and Sheaves” a good followup to Aluffi's “Algebra: Chapter 0”?
Dear @Saal: no,no, tom Dieck is not verbose. He just wants to cover a broad territory in algebraic topology. Another choice is Rotman's Introduction to Algebraic Topology, which is more elementary and very user friendly. The same Rotman wrote a nice introduction to homological algebra, using more category theory, which you might also like.
1d
answered Is “Categories and Sheaves” a good followup to Aluffi's “Algebra: Chapter 0”?
1d
comment Understanding the “shape” of a singular Riemann surface
What do you mean by genus? Anyway, you should complete your curves: your question is ambiguous as it stands since you can take the closure of your curves in $\mathbb P^2$ or take the normalization of that closure.
Jul
26
comment What is a counterexample that a composition of covering maps not a covering map?
Dear @Colin, I'm curious to know what you mean by covering map since I find quite strange that in your definition the composite of two covering maps is a covering map!
Jul
26
comment generalized principal open set
Mike, here are three proofs that the punctured plane is not affine.
Jul
25
comment generalized principal open set
A more accessible reference for 3) might be Eisenbud's Commutative Algebra Corollary 11.4.
Jul
25
answered generalized principal open set
Jul
25
comment Does having a codimension-1 embedding of a closed manifold $M^n \subset \mathbb{R}^{n+1}$ require $M$ to be orientable?
Yes, any closed smooth hypersurface of $\mathbb R^n$ is orientable. See also here.
Jul
25
comment Are closed, properly embedded manifolds of co-dimension 1 in $\mathbb{R}^n$ orientable?
Compactness is irrelevant: see the proof here.
Jul
24
comment Third point of intersection is also a point of inflection?
Yes, I quite agree. Once again: this is a very pretty answer.
Jul
24
comment Third point of intersection is also a point of inflection?
Dear Lubin, in your elegant solution aren't you using that conversely any $3$-torsion point is an inflexion point?
Jul
24
comment Triviality of a vector bundle is an open condition
Dear Mohan, does your section correspond to the trivial line subbundle of $V$ ? And why is your line bundle not trivial in any neighbourhood of $D$ ?
Jul
21
comment Affine varieties over finite fields
Dear @Daniel, you are absolutely right. I hadn't read the OP's incorrectly formulated question attentively enough : my apologies to you for that. Your comment asking about the page in the reference was clearly the correct reaction.
Jul
21
comment Affine varieties over finite fields
To the OP: the variety $V_g$ is described in my comment to @Daniel. It has dimension $3$ and degree $2$. Its only singularity is its summit.
Jul
21
comment Affine varieties over finite fields
Dear @Daniel: if $t$ is the fifth coordinate in $\mathbb{P}_{\mathbb{F}_p}^4$, the OP's equation describes a $3$-dimensional cone $V_g\subset \mathbb{P}_{\mathbb{F}_p}^4$. That cone has as summit the point $(x:y:z:w:t)=(0:0:0:0:1)$ and as base the $2$-dimensional quadric in $\mathbb{P}_{\mathbb{F}_p}^3$ given by the equation $xy-wz=0$.
Jul
20
comment Hartshorne's proof of the exact sequence $\mathbb{Z} \to \operatorname{Cl} X \to \operatorname{Cl} U \to 0$
Your proof is now absolutely correct :+1.