# Tagged Questions

**2**

votes

**0**answers

83 views

### On one class of Euclidean lattices

Let $\Lambda\subset \mathbb Z^3$ be 3D lattice with a basis
$$a_1=\left(\begin{smallmatrix} a_{11} \\ a_{21}\\
a_{31}
\end{smallmatrix}\right),a_2=\left(\begin{smallmatrix} a_{12} \\ a_{22}\\
a_{32}
...

**11**

votes

**7**answers

420 views

### Does the notion of graphs with vertex multiplicity exist?

I need to use graphs where each vertex gets a natural number, $b(v)$, its multiplicity. These numbers indicate how many 'replications' of the vertex we have.
It is actually a way to write in a ...

**16**

votes

**1**answer

756 views

### Surreal exponentiation — are the varying definitions equivalent? If not, is there agreement on which ones are better?

The surreal numbers are sometimes introduced as a place where crazy expressions like $(\omega^2+5\omega-13)^{1/3-2/\omega}+\pi$ (to use the nLab's example) make sense. The problem is, there seem to ...

**2**

votes

**2**answers

565 views

### Non-split groups

I am looking for a reference with definitions on what it means for an algebraic group to be split, quasi-split, and non-split. I would like to see some examples of the different "types".
Thanks,
Tom

**2**

votes

**2**answers

585 views

### On figurate numbers

Do you know a text where I can find a definition of polygonal number that is both geometrically and operationally sound?
I've basically seen two ways in which this topic is approached in the ...

**1**

vote

**4**answers

511 views

### What is the quantity 2(handles)+crosscaps called?

It is well-known that up to homeomorphism, the complete set of orientable surfaces is $\lbrace S_g : g=0,1,\dots \rbrace$, where $S_g$ is the sphere with $g$ handles. The complete set of ...

**5**

votes

**0**answers

258 views

### Why is Pic^0(C) of a curve C a variety?

Let $C$ be an abstract non-singular curve.
I'm having a hard time finding a reference for why $\text{Pic}^0(C)$ is a variety.
Any pointers towards a reference would be appreciated.

**23**

votes

**1**answer

2k views

### What is Serre's condition (S_n) for sheaves?

The Serre's condition $(S_n)$, especially $(S_2)$, has been mentioned in a few MO answers: see here and here for example. I am pretty sure I have seen it in other questions as well, but could not ...