SMOOTH PROJECTIVE SYMMETRIC VARIETIES WITH PICARD NUMBER ONE

Author:

RUZZI ALESSANDRO1

Affiliation:

1. Dipartimento di Matematica G. Castelnuovo, Università la Sapienza, P. le Aldo Moro 5, 00185 Roma, Italy

Abstract

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover, we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Horospherical two-orbit varieties as zero loci;Proceedings of the American Mathematical Society;2023-05-05

2. Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One;Mathematics;2021-01-05

3. Kähler geometry of horosymmetric varieties, and application to Mabuchi’s K-energy functional;Journal für die reine und angewandte Mathematik (Crelles Journal);2020-06-01

4. K-stability of Fano spherical varieties;Annales scientifiques de l'École normale supérieure;2020

5. On the deformation rigidity of smooth projective symmetric varieties with Picard number one;Comptes Rendus Mathematique;2019-11

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