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On syzygies of divisors on rational normal scrolls
Author(s) -
Park Euisung
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300085
Subject(s) - mathematics , betti number , divisor (algebraic geometry) , variety (cybernetics) , projective variety , diagram , pure mathematics , resolution (logic) , degree (music) , statistics , artificial intelligence , computer science , physics , acoustics
In this paper, we study the minimal free resolution of a nondegenerate projective variety X ⊂ P rwhen X is contained in a variety Y of minimal degree as a divisor. Such a variety is of interest because of its extremal behavior with respect to various properties. The graded Betti diagram of X has been completely known only when X is arithmetically Cohen‐Macaulay. Our main result in the present paper provides a detailed description of the graded Betti diagram of X for the case where X is not arithmetically Cohen‐Macaulay.