12
votes
1answer
798 views
+100

A question about certain sets of permutations of the ordered pairs $(1,1),(1,2),\cdots,(1,n),\cdots,(n,1),(n,2),\cdots,(n,n)$

Let $n>1$ be a given positive integer. For any $0\leq k\leq n^2$, let $A_k$ be the set of permutations $((i_1,j_1),(i_2,j_2),\cdots,(i_{n^2},j_{n^2}))$ of the ordered pairs ...
9
votes
2answers
470 views
+100

Tangent space of Hilbert scheme

We have the following theorem: Let $X$ be a projective scheme over an algebraically closed field $k$, and $Y \subset X$ a closed subscheme with Hilbert polynomial $P$. Then$$T_{[Y]}\text{Hilb}_P (X) ...
6
votes
0answers
195 views
+50

Thom Class of tensor bundles

Suppose $\xi$ and $\eta$ are oriented vector bundles over a CW-complex $B$. Is it possible to express the Thom class (with ${\mathbb Z}$ coefficients) of $\xi\otimes \eta$ or even ${\rm Sym}^2(\xi)$ ...
23
votes
0answers
524 views
+100

partition of infinite word onto permitted words

Consider words over binary alphabet $\{0,1\}$. Let $M$ be a set of finite words such that $M$ contains at least $c\cdot 2^n$ words of length $n$ for all large enough $n$ (for a constant $c$, ...
10
votes
2answers
292 views
+300

2-dimensional sublattices with all vectors having very big square (in absolute value)

QUESTION: Let $\Lambda\times\Lambda\rightarrow {\Bbb Z}$ be a lattice, that is, ${\Bbb Z}^n$ with a non-degenerate integer quadratic form, not definite, not necessarily unimodular, $n>2$. I want ...
12
votes
1answer
228 views
+50

Which sequential colimits commute with pullbacks in the category of topological spaces?

This question was asked on math.stackexchange.com without a reaction. Given diagrams of topological spaces $$X_0\rightarrow X_1\rightarrow\ldots$$ $$Y_0\rightarrow Y_1\rightarrow\ldots$$ ...