L-equivalences via Symplectic and F₄ Grassmannians

2025/12/18 by Noden, Ivan
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2512.16507

openalex publication_date 2025/12/18 · openalex created_date 2025/12/21 · openalex updated_date 2026/07/28

Abstract

Using a construction of Kanemitsu from [9] and observations by Rampazzo in [19], we find examples of zero divisors in the Grothendieck ring of varieties by taking the zero loci of sections of vector bundles over symplectic and F₄ Grassmannians. These zero divisors yield instances of non-trivially L-equivalent Calabi-Yau varieties. This methodology is inspired by a similar process performed by Ito et al. on G₂ Grassmannians in [8].

Citations

• Derived equivalence for the simple flop of type D₅
• New counterexamples to the birational Torelli theorem for Calabi--Yau manifolds
• Mukai pairs and simple K-equivalence
• Torelli problem for Calabi-Yau threefolds with GLSM description
• The class of the affine line is a zero divisor in the Grothendieck ring: via G₂-Grassmannians

Related

• The class of the affine line is a zero divisor in the Grothendieck ring: via G₂-Grassmannians
• An example of birationally inequivalent projective symplectic varieties which are D-equivalent and L-equivalent
• Class of the affine line is a zero divisor in the Grothendieck ring
• L-equivalence and Fourier--Mukai partners of cubic fourfolds
• G₂-Grassmannians and derived equivalences