Irreducible symplectic varieties with a large second Betti number

2024/10/02 by Yuchen Liu, Liu, Yuchen, Zhiyu Liu +3 · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2410.01566

openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a general result on the existence of irreducible symplectic compactifications of non-compact Lagrangian fibrations. As an application, we show that the relative Jacobian fibration of cubic fivefolds containing a fixed cubic fourfold can be compactified by a ℚ-factorial terminal irreducible symplectic variety with the second Betti number at least 24, and admits a Lagrangian fibration whose base is a weighted projective space. In particular, it belongs to a new deformation type of irreducible symplectic varieties.

Cited by

• Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture
• Abelian fiber spaces and their Tate-Shafarevich twists with sections

Related

• Lagrangian fibrations for IHS fourfolds
• Lagrangian fibrations on symplectic fourfolds
• A new six dimensional irreducible symplectic variety
• Compactifying Lagrangian fibrations
• Irreducible symplectic varieties via relative Prym varieties