1 results
Models and integral differentials of hyperelliptic curves
- Part of
-
- Journal:
- Glasgow Mathematical Journal / Volume 66 / Issue 2 / May 2024
- Published online by Cambridge University Press:
- 18 March 2024, pp. 382-439
- Print publication:
- May 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
Let
$C\; : \;y^2=f(x)$ be a hyperelliptic curve of genus 
$g\geq 1$, defined over a complete discretely valued field 
$K$, with ring of integers 
$O_K$. Under certain conditions on 
$C$, mild when residue characteristic is not 
$2$, we explicitly construct the minimal regular model with normal crossings 
$\mathcal{C}/O_K$ of 
$C$. In the same setting we determine a basis of integral differentials of 
$C$, that is an 
$O_K$-basis for the global sections of the relative dualising sheaf 
$\omega _{\mathcal{C}/O_K}$.
