Extremal Contraction of Projective Bundles

2024/09/08 by Ashima Bansal, Supravat Sarkar, Bansal, Ashima +3 · 1 citation
Mathematics · Physics and Astronomy · #14E05 #14E30 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2409.05091

openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we explore the extremal contractions of several projective bundles over smooth Fano varieties of Picard rank 1. We provide a whole class of examples of projective bundles with smooth blow-up structures, derived from the notion of drums which was introduced by Occhetta-Romano-Conde-Wiśniewski to study interaction with ℂ^*-actions and birational geometry. By manipulating projective bundles, we give a simple geometric construction of the rooftop flip, which was introduced recently by Barban-Franceschini. Additionally, we obtain analogues of some recent results of Vats in higher dimensions. The list of projective bundles we consider includes all globally generated bundles over projective space with first Chern class 2. For each of them, we compute the nef and pseudoeffective cones.

Cited by

• Automorphisms of punctual Hilbert schemes and symmetric powers of varieties

Related

• Smooth blow up structures on projective bundles
• On singular Fano varieties with a divisor of Picard number one
• Fano manifolds obtained by blowing up along curves with maximal Picard number
• Morelli-Włodarczyk cobordism and examples of rooftop flips
• On weak Fano manifolds with small contractions obtained by blow-ups of a product of projective spaces