# Tagged Questions

**1**

vote

**1**answer

161 views

### Does $\mathbb P^1 \times \mathbb P^1$ admit an Ulrich bundle?

In an answer to a MathOverflow question on the following link
Vector bundles on $\mathbb{P}^1\times\mathbb{P}^1$, it is mentioned that $\mathbb P^1 \times \mathbb P^1$ has an Ulrich sheaf. However, ...

**2**

votes

**1**answer

508 views

### Spectral sequence of symmetric or exterior algebras?

This question is inspired by Hartshorne's exercise II.5.7 (c-d): the problem reads:
Let $0\rightarrow \mathcal{F}'\rightarrow\mathcal{F}\rightarrow\mathcal{F}''\rightarrow0$ be a short exact sequence ...

**10**

votes

**4**answers

565 views

### Algebraic analogue of the Moebius bundle over the circle

Let $R$ be the ring $R[X,Y]/(X^2+Y^2−1)$. The space of $\mathbb{R}$-rational points of the affine scheme associated to $R$ is the topological circle $S^1$.
An algebraic vector bundle over $R$ is an ...

**4**

votes

**3**answers

1k views

### The correspondence between affine vector bundles and f.g. projective modules

The definition of a (geometric) vector bundle over a scheme $X$ can be rewritten as follows in terms of 'not-so-geometrical algebra' if $X=Spec R$ is affine and if I am not missing something.
A ...

**2**

votes

**2**answers

253 views

### Is a submodule of the sheaf of sections of a smooth vector bundle necessarily finitely generated?

Let $X$ be a finite-dimensional smooth manifold, $\mathcal C^\infty(X)$ its algebra of smooth functions, $V\to X$ a finite-dimensional smooth vector bundle, and $\Gamma(V)$ the space of smooth ...

**16**

votes

**5**answers

1k views

### A ring such that all projectives are stably free but not all projectives are free?

This question is motivated by this recent question. Suppose $R$ is commutative, Noetherian ring and $M$ a finitely generated $R$-module. Let $FD(M)$ and $PD(M)$ be the shortest length of free and ...

**1**

vote

**6**answers

1k views

### Differences between reflexives and projectives modules

Let R be a normal noetherian domain.
What is the difference between a finitely generated reflexive module and a finitely generated projective module?
Can anybody recommend any references or make ...