@article{oai:u-hyogo.repo.nii.ac.jp:00006215,
 author = {遊佐, 毅 and Usa, Takeshi},
 issue = {31},
 journal = {兵庫県立大学大学院物質理学研究科・生命理学研究科研究報告, Reports of Graduate School of Material Science and Graduate School of Life Science, University of Hyogo},
 month = {Feb},
 note = {先の論文［10］の予想2.4を肯定的に解決できたので、その証明を与える。その主張とは、P^4の種数5の標準曲線を全て含むヒルベルト・スキームの普遍族から誘導された滑らかな底アフィン曲線B上の平坦族が閉点b_0上の閉ファイバーとしてトリゴナル曲線を持つ時、ファイバーの第一シチジーの次数3の極小生成系を記述する O_B-加群{\mathscr{T}}^{1,1}_{3} は、点 b_0 における底曲線 B とトリゴナル曲線に対応する因子の滑らかな分岐との交わりの横断性を探知出来るというものである。
We consider a smooth affine curve B in the Hilbert scheme Hilb_P^{A(m)} of P=P^4 associated with a Hilbert polynomial A(m)=8m-4, which includes all the canonical curves (i.e. non-singular projective and non-hyperelliptic curves of g ≧3 embedded into projective spaces by their complete canonical linear systems) of genus 5 in its universal family. Assume that from the universal family of Hilb_P^{A(m)}, the curve B induces a family f: {\frak X} →B of canonical curves with genus 5 and all the closed fibers are non-trigonal ones except only one trigonal closed fiber over a closed point b_0 ∈ B. In this article, we give a proof for an affirmative result on Conjecture 2.4 of［10］which claims that the structure of O_B-module {\mathscr{T}}^{1,1}_{3} describing the first syzygies in degree 3 of the fibers can detect the transversality of the intersection at the point b_0 by the base curve B and a smooth branch of the divisor corresponding to the trigonal ones.},
 pages = {1--11},
 title = {種数５の標準曲線の族とシチジーの退化（2）},
 year = {2021},
 yomi = {ウサ, タケシ}
}