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EnglishThe goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms, and Borel-fixed ideals of maximal minors. The main tools are Gröbner bases and Sagbi deformation.
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| Titolo: | Linear resolutions of powers and products |
| Autori: | |
| Data di pubblicazione: | 2017 |
| Abstract: | The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms, and Borel-fixed ideals of maximal minors. The main tools are Gröbner bases and Sagbi deformation. |
| Handle: | http://hdl.handle.net/11567/884592 |
| Appare nelle tipologie: | 02.01 - Contributo in volume (Capitolo o saggio) |
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