On supported deformations and birational isotriviality

2025/06/08 by Luca Rizzi, Rizzi, Luca, Francesco Zucconi +1
Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Elasticity and Wave Propagation #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2506.07059

openalex publication_date 2025/06/08 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

It is well known that the general fibers of a fibration f\colon X→ B are isomorphic if the general Kodaira-Spencer class vanishes. In this paper we consider the birational analogue when the general Kodaira-Spencer class is supported on a divisor.

Citations

• Global Kodaira Spencer class and Massey products
• Massey products and Fujita decomposition over higher dimensional base
• Fujita decomposition and Massey product for fibered varieties
• On birational trivial families and Adjoint quadrics
• Codimension 1 foliations with numerically trivial canonical class on singular spaces
• Differential forms and quadrics of the canonical image
• On deformations of curves supported on rigid divisors
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• General curves on algebraic surfaces
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Related

• Birational geometry of algebraic varieties, fibred into Fano double\n spaces
• Fibered stable varieties
• Kodaira additivity, birational isotriviality and specialness
• Deformation rigidity for projective manifolds and isotriviality of smooth families
• Stability of fibrations over one-dimensional bases