Abstract
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation between this equivalence of categories and certain duality functors. We use our results to explicitly construct examples of semi-stable sheaves on degenerating families of elliptic curves.
| Original language | English |
|---|---|
| Pages (from-to) | 283-306 |
| Number of pages | 24 |
| Journal | Manuscripta Mathematica |
| Volume | 120 |
| Issue number | 3 |
| Early online date | 3 Jun 2006 |
| DOIs | |
| Publication status | Published - Jun 2006 |
Keywords
- 18E30
- 14H60
- 14H20
- 14J27
- 14H10
- Fourier–Mukai
- fibrations
- singular
- non-projective
- Grothendieck duality
- skew–commutativity relation
- duality functors
- semi-stable sheaves
- elliptic curves