### Abstract

In this article we study the problem to determine all occurring Betti diagrams of varieties X ⊂ P^{r} of almost minimal degree, i.e., deg(X) = codim(X,P^{r}) + 2. We describe a realistic picture of how many different kind of Betti diagrams exist at all (Theorem 3.1). By means of the computer algebra system "SINGULAR", we obtain a complete list of all occurring Betti diagrams in the cases where codim(X,P^{r}) ≤ 8.

Original language | English |
---|---|

Pages (from-to) | 1001-1015 |

Number of pages | 15 |

Journal | Journal of the Korean Mathematical Society |

Volume | 48 |

Issue number | 5 |

Publication status | Published - 2011 Sep 1 |

### Fingerprint

### Keywords

- Betti number
- Minimal free resolution
- Rational normal scroll
- Varieties of low degree

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of the Korean Mathematical Society*,

*48*(5), 1001-1015.

**Classification of betti diagrams of varieties of almost minimal degree.** / Lee, Wanseok; Park, Euisung.

Research output: Contribution to journal › Article

*Journal of the Korean Mathematical Society*, vol. 48, no. 5, pp. 1001-1015.

}

TY - JOUR

T1 - Classification of betti diagrams of varieties of almost minimal degree

AU - Lee, Wanseok

AU - Park, Euisung

PY - 2011/9/1

Y1 - 2011/9/1

N2 - In this article we study the problem to determine all occurring Betti diagrams of varieties X ⊂ Pr of almost minimal degree, i.e., deg(X) = codim(X,Pr) + 2. We describe a realistic picture of how many different kind of Betti diagrams exist at all (Theorem 3.1). By means of the computer algebra system "SINGULAR", we obtain a complete list of all occurring Betti diagrams in the cases where codim(X,Pr) ≤ 8.

AB - In this article we study the problem to determine all occurring Betti diagrams of varieties X ⊂ Pr of almost minimal degree, i.e., deg(X) = codim(X,Pr) + 2. We describe a realistic picture of how many different kind of Betti diagrams exist at all (Theorem 3.1). By means of the computer algebra system "SINGULAR", we obtain a complete list of all occurring Betti diagrams in the cases where codim(X,Pr) ≤ 8.

KW - Betti number

KW - Minimal free resolution

KW - Rational normal scroll

KW - Varieties of low degree

UR - http://www.scopus.com/inward/record.url?scp=80052600475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052600475&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80052600475

VL - 48

SP - 1001

EP - 1015

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

SN - 0304-9914

IS - 5

ER -