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2d

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Triangulated category of singularities of quotient
The right term is "triangulated category of singularities" 
Dec 24 
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Blowups of $\mathbb{P}^{n3}$ and $(\mathbb{P}^1)^{n3}$
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 
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Properties of finite quotients of quasiprojective varieties
@Sasha Isn't $X/G$ always the categorical quotient in the quasiprojective case? 
Nov 30 
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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 
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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 
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Lower semicontinuity of naive fiber size
This is not hard an is a typical Shafarevichstyle 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 
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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 
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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 
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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 principalness? 
May 15 
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Reference needed: Homology of the blowup
Do you put any restrictions on $V$? 
May 14 
answered  “Exactness” of groupify functor 
Mar 15 
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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 $n^21$, 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 