Explicit minimal embedded resolutions of divisors on models of the projective line
Let K be a discretely valued field with ring of integers O K with perfect residue field. Let K ( x ) be the rational function field in one variable. Let P O K 1 be the standard smooth model of P K 1 with coordinate x . Let f ( x ) ∈ O K [ x ] be a squarefree polynomial with corresponding divisor of...
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| Veröffentlicht in: | Research in number theory 2022-06, Vol.8 (2), Article 27 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
K
be a discretely valued field with ring of integers
O
K
with perfect residue field. Let
K
(
x
) be the rational function field in one variable. Let
P
O
K
1
be the standard smooth model of
P
K
1
with coordinate
x
. Let
f
(
x
)
∈
O
K
[
x
]
be a squarefree polynomial with corresponding divisor of zeroes
div
0
(
f
)
on
P
O
K
1
. We give an explicit description of the minimal embedded resolution
Y
of the pair
(
P
O
K
1
,
div
0
(
f
)
)
by using Mac Lane’s theory to write down the discrete valuations on
K
(
x
) corresponding to the irreducible components of the special fiber of
Y
. |
|---|---|
| ISSN: | 2522-0160 2363-9555 |
| DOI: | 10.1007/s40993-022-00323-y |