On the normal sheaf of Gorenstein curves

• Ano de defesa: 2022
• Autor(a) principal: Júnio Teles dos Santos
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Minas Gerais; Brasil; ICEX - INSTITUTO DE CIÊNCIAS EXATAS; Programa de Pós-Graduação em Matemática; UFMG
• Palavras-chave em Português: Gorenstein curves; Scrolls; Stability of normal sheafs; Upper semicontinuity; Matemática - Teses; Curvas de Gorenstein - Teses; Semicontinuidade - Teses; Feixes Normais - Teses
• Link de acesso: http://hdl.handle.net/1843/47372; https://orcid.org/0000-0001-6772-6998

We show that any tetragonal Gorenstein integral curve is a complete intersection in its respective 3-fold rational normal scroll S, implying that the normal sheaf on C embedded in S, and in P g-1 as well, is unstable for g ≥ 5, provided that S is smooth. We also compute the degree of the normal sheaf of any singular reduced curve in terms of the Tjurina and Deligne numbers, providing a semicontinuity of the degree of the normal sheaf over suitable deformations, revisiting classical results of the local theory of analytic germs.