A hypersurface X ⊂ Pn is said to be free if its associated sheaf TX of vector fields tangent to X is a free OPn-module. So far few examples of free hypersurfaces are known. In this short note, we reinterpret Saito’s criterion of freeness in terms of multiple eigenschemes (ME) and as application we construct huge families of new examples of free reduced hypersurfaces in Pn. All of them are union of hypersurfaces in a suitable pencil.
Saito’s theorem revisited and application to free pencils of hypersurfaces / Di Gennaro, Roberta; Miró-Roig, Rosa. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1088-6826. - 153:9(2025), pp. 3663-3675. [10.1090/proc/17240]
Saito’s theorem revisited and application to free pencils of hypersurfaces
Di Gennaro, Roberta;
2025
Abstract
A hypersurface X ⊂ Pn is said to be free if its associated sheaf TX of vector fields tangent to X is a free OPn-module. So far few examples of free hypersurfaces are known. In this short note, we reinterpret Saito’s criterion of freeness in terms of multiple eigenschemes (ME) and as application we construct huge families of new examples of free reduced hypersurfaces in Pn. All of them are union of hypersurfaces in a suitable pencil.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
