# Tagged Questions

**1**

vote

**0**answers

121 views

### Uniqueness of lifting of very ample line bundle on smooth proper surfaces over DVR

Let $R$ be a complete Henselian discrete valuation ring of characteristic 0, $X_R$ be a surface smooth, proper and flat over $R$. Assume that the residue field $k$ of $R$ is algebraically closed of ...

**1**

vote

**2**answers

365 views

### Equation for simple Jacobian of a genus two curve

Let $X$ be a curve of genus two over a field $k$ with a $k$-rational point. Let $J$ be the Jacobian of $X$.
Can we write down an explicit equation for the abelian surface $J$?
I know $X$ can be ...

**2**

votes

**1**answer

247 views

### Does each finite morphism of curves have a model whose minimal resolution is semi-stable

Let $\pi:Y\to X$ be a finite morphism of smooth projective geometrically connected curves over a number field $K$.
Question. Does there exist a finite field extension $L/K$ and a regular model ...

**7**

votes

**2**answers

458 views

### The number of singular fibres of a semi-stable arithmetic surface over \Z

This is an arithmetic follow-up to my previous question Does there exist a non-trivial semi-stable curve of genus >1 with only 4 singular fibres
Let $k$ be an algebraically closed field and let ...