Calabi-Yau Structures, Spherical Functors, and Shifted Symplectic Structures

Ludmil Katzarkov; Pranav Pandit; Theodore Spaide

arxiv: 1701.07789 · v2 · pith:O7HWP3WEnew · submitted 2017-01-26 · 🧮 math.AG · math.SG

Calabi-Yau Structures, Spherical Functors, and Shifted Symplectic Structures

Ludmil Katzarkov , Pranav Pandit , Theodore Spaide This is my paper

classification 🧮 math.AG math.SG

keywords structuresgeometrycalabi-yauderivedsymplecticcertainnotionshifted

0 comments

read the original abstract

A categorical formalism is introduced for studying various features of the symplectic geometry of Lefschetz fibrations and the algebraic geometry of Tyurin degenerations. This approach is informed by homological mirror symmetry, derived noncommutative geometry, and the theory of Fukaya categories with coefficients in a perverse Schober. The main technical results include (i) a comparison between the notion of relative Calabi-Yau structures and a certain refinement of the notion of a spherical functor, (ii) a local-to-global gluing principle for constructing Calabi-Yau structures, and (iii) the construction of shifted symplectic structures and Lagrangian structures on certain derived moduli spaces of branes. Potential applications to a theory of derived hyperk\"ahler geometry are sketched.

This paper has not been read by Pith yet.

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

From Finite-Node Conifold Geometry to BPS Structures III: Mediated Triangle Transport and Graded Interaction Data
math.AG 2026-05 unverdicted novelty 5.0

Mediated triangle transport yields graded interaction polynomials I_Σ^gr from conifold state data, extending binary support structures for BPS and stability theory.