Questions tagged [ag.algebraic-geometry]
Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
41 questions from the last 30 days
2
votes
0
answers
38
views
What are the terms in the Eagon Northcott complex?
Let $E \to F$ be a map of vector bundles on a scheme $X$ of ranks $e, f$ (actually, I hope $X$ may be a stack here). Suppose $e \leq f$. I want to describe the locus $D \subseteq X$ where $E \to F$ ...
- 1,154
0
votes
0
answers
165
views
Finding all integer solutions to a family of elliptic curves depending on a parameter $n$
Consider this equation
\begin{equation}
y^2 = x^3 + (36n + 27)^2 \cdot x^2 + (15552 n^3 + 34992 n^2 + 26244 n + 6561) \cdot x + (46656 n^4 + 139968 n^3 + 157464 n^2 + 78713 n + 14748)
\end{equation}
...
- 139
0
votes
0
answers
114
views
symplectic resolution of K theoretic coulomb branch
Consider the type $A_n$ quiver with gauge group $G=\prod_i \mathrm{GL(V_i)}$ and representation $N=\oplus_i \mathrm{Hom(N_i, N_{i+1})}$, will the K-theoretic Coulomb branch $Spec(\mathrm{K}^{ G(\...
- 591
2
votes
1
answer
94
views
relation between eventual coconnectiveness and tor amplitude of $f$ and cotangent complex of $f$ be perfect
I was currently reading derived geometry from Lurie's thesis and DAG's. I am wondering about the following.
Let $f:X \to Y$ be a morphism of derived Deligne-Mumford stacks. Let the cotangent complex $...
- 1,619
4
votes
1
answer
333
views
How many translation lines do we need to have a Moufang plane?
A projective plane $\mathscr{P}$ is called a Moufang plane if it is a translation plane with respect to all of its lines. In other words, a Moufang plane is a projective plane such that the minor ...
- 69.2k
11
votes
1
answer
328
views
Is there a noetherian ring having infinitely many residue fields of size $q$?
Fix some finite field $F$. Is there a (commutative) noetherian ring $R$ having infinitely many residue fields isomorphic to $F$?
By replacing $R$ with $R/pR$, with $p$ being the characteristic of $F$, ...
- 3,328
1
vote
1
answer
227
views
Question on monotonicity of a norm-like function for matrices
Let $P_1,P_2$ be two real orthogonal projections on $\mathbb R^n$, and assume that they are permutation similar. More specifically, assume that each of them is permutation similar to a block diagonal ...
- 857
4
votes
1
answer
173
views
Question on power-nonnegative matrix
Let $P_1,P_2\in M_n(\mathbb R)$ be two orthogonal projections, i.e., $P_1^2=P_1=P_1', P_2^2=P_2=P_2'$ and assume that they are unitarily similar.
Let
$$
A=(P_1P_2)\circ(P_2P_1),
$$
where $\circ$ ...
- 857
5
votes
1
answer
264
views
Infinitesimal neighbourhoods for derived schemes
I am currently reading basics of deformation theory from Hartshorne's book on Deformation theory. I understood how the n'th infinitesimal neighbourhood of diagonal is defined for classical schemes. My ...
- 1,619
3
votes
0
answers
140
views
Operator-valued Schwartz function
Let $\mathcal{H}$ be a Hilbert Space and let $\mathcal{B}$ be the Hausdorff LCS of bounded operators in $\mathcal{H}$ equipped with the WOT-topology.
Let $A(t), t \in \mathbb{R}$ be $\mathcal{B}$-...
- 161
1
vote
0
answers
251
views
A question on rank two vector bundles on the real two sphere
Let $k$ be the real numbers, $K$ the compex numbers and let $x,y,z$ be independent variables over $k$. Let $f:=x^2+y^2+z^2-1$ and let $A:=k[x,y,z]/(f), B:=K[x,y,z]/(f)$ and let $S:=Spec(A)$.
In a ...
- 481
16
votes
1
answer
418
views
Finite projective planes of order $9$ and quasi-fields
Recently, I got interested in finite projective planes. I'm not an expert, so I apologise in advance if some of my questions are very easy for people working in the area.
I would like to understand ...
- 69.2k
14
votes
2
answers
978
views
Geometric intuition of Gorenstein rings
As part of a course in commutative algebra or algebraic geometry, one will generally learn that, for a Noetherian local ring:
regular $\Rightarrow$ complete intersection $\Rightarrow$ Gorenstein $\...
- 40.2k
2
votes
0
answers
230
views
Non-vanishing of quantum cohomology
Let $(X)$ now be a smooth projective variety over $(\mathbb{C})$, and consider genus-zero Gromov–Witten invariants. Define
$[I(t,\alpha,\beta,\gamma)
\sum_{d \in H_2(X,\mathbb{Z})}
\left\langle \alpha,...
- 121
3
votes
0
answers
210
views
Higher Chow groups of singular scheme over Z
Let $X$ be a separated, finite type scheme over $\operatorname{Spec}\mathbb{Z}$. I want to know if all of the nice properties of the cycle complex of a smooth equidimensional variety over a field $k$ (...
- 251