### Abstract

In this paper, we study how the minimal free resolution of a closed subscheme X ⊂ ℙ^{r} relates to that of a linear section X ∩ Λ ⊂ Λ = ℙ^{s} (0 < s < r). Our main result implies that the shape of the final non-zero row of the Betti diagram of X is preserved under taking the zero-dimensional and one-dimensional linear sections.

Original language | English |
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Pages (from-to) | 1831-1836 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

- Linear section
- Minimal free resolution

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics