随伴形式とspherical多様体の超曲面のトレリ型問題

伴随形式和球流形超曲面的网格型问题

• 批准号: 19F19780
• 负责人: 小木曽 啓示
• 金额: $ 1.41万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2019
• 资助国家: 日本
• 起止时间: 2019-11-08 至 2022-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-19F19780/
• 关键词: Torelli problem; semi-stable fibration; local system; Fujita decomposition; 無限小Torelli問題; hypersurfaces; Massey product; 有理等質多様体

Doctor Luca Rizzi has worked on hypersurfaces in special subclasses of spherical varieties. In particular Doctor Rizzi has proved the explicit equivalence between the theory of Massey products and the theory of the infinitesimal Torelli problem for smooth hypersurfaces in rational homogeneous varieties with Picard number one. In the same paper Doctor Rizzi has also been able to prove an infinitesimal Torelli theorem for smooth hypersurfaces in log-parallelizable varieties.Doctor Rizzi has also worked on semistable fibrations of projective varieties and studied the monodromy associated to local systems of relative differential forms. Doctor Rizzi has given conditions on the finiteness of this monodromy. This is related to semi-ampleness problems and to an important conjecture by Fujita.

卢卡·里兹（Luca Rizzi）医生曾在特殊的球形品种特殊子类中工作。特别是，Rizzi医生已证明Massey产品理论与无限的Torelli问题之间的明确等效性，用于具有Picard第一的合理均质品种中的平滑性超浮标。在同一篇论文中，Rizzi医生还能够证明无限的Torelli定理，用于在原木可行的品种中进行平滑的超曲面。DoctorRizzi还研究了投影品种的可半固定纤维，并研究了与相对差异形式的局部系统相关的单片。 Rizzi医生给出了这种单片的有限条件。这与藤田的半扩增性问题和重要的猜想有关。

项目成果

Weighted Fano varieties and infinitesimal Torelli problem

加权 Fano 簇和无穷小 Torelli 问题

• 发表时间: 2019
• 期刊: J. Geom. Phys.
• 作者: Fatighenti;Enrico; Rizzi;Luca; Zucconi;Francesco
• 通讯作者: Francesco

Francesco Differential forms and quadrics of the canonical image

Francesco 规范图像的微分形式和二次曲面

• 发表时间: 2020
• 期刊: Ann. Mat. Pura Appl.
• 作者: Rizzi;Luca;Zucconi;Francesco
• 通讯作者: Francesco

Fujita decomposition and Massey product for fibered varieties

纤维品种的藤田分解和梅西积

• DOI: 10.1017/nmj.2021.15
• 发表时间: 2021
• 期刊: Nagoya Mathematical Journal
• 影响因子: 0.8
• 作者: L. Rizzi;F. Zucconi
• 通讯作者: F. Zucconi

University of Udine(イタリア)

乌迪内大学（意大利）

Udine大学(イタリア)

乌迪内大学（意大利）