We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah and Tu's results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.
Relatively stable bundles over elliptic fibrations / Bartocci, C.; Bruzzo, U.; Hernandez-Ruiperez, D.; Minoz Porras, J. M.. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 238:1(2002), pp. 23-36. [10.1002/1522-2616(200205)238:1<23::AID-MANA23>3.0.CO;2-#]
Relatively stable bundles over elliptic fibrations
Bruzzo, U.;
2002-01-01
Abstract
We consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah and Tu's results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
