Linearity defect and Betti splittings

Thời gian: 14:00 đến 15:00 Ngày 19/04/2016

Địa điểm: C2-714

Báo cáo viên: Nguyen Dang Hop

Tóm tắt:

Betti splittings were introduced by Francisco, Hà and Van Tuyl to study free resolutions of monomial ideals. We present the application of Betti splittings to two results due to Fröberg and Francisco-Van Tuyl. Fröberg proves that the edge ideal of a graph G has linear resolution if and only if the complement of G is chordal. On the other hand, Francisco and Van Tuyl (Some families of componentwise linear monomial ideals) prove that for any union of three coordinate fat linear subpaces, the corresponding defining ideal is componentwise linear. In both case, we can recover and generalize the known result using suitable Betti splittings.