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2d
comment Triangulated category of singularities of quotient
The right term is "triangulated category of singularities"
Dec
24
comment Blow-ups of $\mathbb{P}^{n-3}$ and $(\mathbb{P}^1)^{n-3}$
I like the trick with moving "extra" points, but it would still be nice to have a purely geometric construction.
Dec
18
answered On understanding Orlov's LG B model
Dec
8
comment Properties of finite quotients of quasi-projective varieties
@Sasha Isn't $X/G$ always the categorical quotient in the quasi-projective case?
Nov
30
comment Cartier divisor on a double cover
@LiYutong If you double this line, it's by no means equivalent to $\pi^*D$.
Nov
21
answered Hartshorne Proposition III 8.1
Nov
18
awarded  Yearling
Oct
8
comment Soft question: beginners reference to moduli spaces
The book is indeed a brother of "Methods of Homological Algebra: Vol. II". Well, we still have drafts and, say, Behrend's lectures mentioned by Piotr.
Oct
8
comment Lower semicontinuity of naive fiber size
This is not hard an is a typical Shafarevich-style argument. A tiny improvement to the algebraic counterpart is to state explicitly that given a normal domain $A$ and a finite extension $L$ of its field of fractions $K$ an element $u\in L$ is integral over $A$ iff its minimal polynomial is defined over $A$ (in particular, it exists). Of course, this is essentially Lemma 1.
Oct
8
comment About $\mathbb P^1_\mathbb C$ contained in a surface
I'd say that your last paragraph is much more illuminating than doing things explicitly.
Sep
26
answered Spec of an injective ring map contains minimal primes in its image?
Sep
26
comment pencil of quadrics consisting of singular quadrics
@MartinBright As far as I remember, Miles's brilliant thesis deals with the smooth case (allowing only the simplest cones).
Sep
26
answered pencil of quadrics consisting of singular quadrics
Aug
27
answered linear section of codimension $k+1$ of a variety of dimension $k$
Aug
25
comment if V(f) is irreducible, then how to show that the polynomial f itself is irreducible?
This is not a research level question.
Jun
4
answered Why does restriction of Weil divisors “clearly” preserve principal-ness?
May
15
comment Reference needed: Homology of the blow-up
Do you put any restrictions on $V$?
May
14
answered “Exactness” of groupify functor
Mar
15
comment Dimension of a commuting nilpotent variety
I'd say that this is a no so trivial question. Namely, if you omit the "commute with $A$" condition, you get the variety of commuting nilpotent matrices. Its dimension is $n^2-1$, which is not obvious (see "The Variety of Pairs of Commuting Nilpotent Matrices is Irreducible" by Volodia Baranovsky).
Feb
21
answered Easy to state applications of dimension theory in algebraic geometry