Twisted Fourier–Mukai partners of Enriques surfaces
Bridgeland and Maciocia showed that a complex Enriques surface X has no Fourier–Mukai partners apart from itself: that is, if D b ( X ) ≅ D b ( Y ) then X ≅ Y . We extend this to twisted Fourier–Mukai partners: if α is the non-trivial element of Br ( X ) = Z / 2 and D b ( X , α ) ≅ D b ( Y , β ) , t...
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| Veröffentlicht in: | Mathematische Zeitschrift 2021-04, Vol.297 (3-4), p.1239-1247 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Bridgeland and Maciocia showed that a complex Enriques surface
X
has no Fourier–Mukai partners apart from itself: that is, if
D
b
(
X
)
≅
D
b
(
Y
)
then
X
≅
Y
. We extend this to twisted Fourier–Mukai partners: if
α
is the non-trivial element of
Br
(
X
)
=
Z
/
2
and
D
b
(
X
,
α
)
≅
D
b
(
Y
,
β
)
, then
X
≅
Y
and
β
is non-trivial. Our main tools are twisted topological K-theory and twisted Mukai lattices. |
|---|---|
| ISSN: | 0025-5874 1432-1823 |
| DOI: | 10.1007/s00209-020-02555-z |