Proves Gamma conjecture II for del Pezzo surfaces by establishing a global Gamma-I property that propagates from one (SR) point and relating it to non-semisimple cases.
Birational Invariants from Hodge Structures and Quantum Multiplication
10 Pith papers cite this work. Polarity classification is still indexing.
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Verra fourfolds have a distinct small quantum cohomology ring implying they are never birational to very general cubic or Gushel-Mukai fourfolds, with primitive cohomology matching a K3 surface when birational.
Smooth quartic threefolds are symplectically irrational, shown via an obstruction from big quantum cohomology eigenvalue multiplicities that is invariant under symplectic operations.
Defines naive atomic decompositions and checks a naive version of Iritani's blowup formula in computable examples.
A projection of the variation morphism defines an intersection-space Hodge atom shadow package for Calabi-Yau conifolds, yielding a middle-degree IC-intersection-space defect of rank 202 for the 125-node quintic.
Constructs a canonical rigid-flexible decomposition of Hodge atoms for conifold degenerations of Calabi-Yau threefolds, with the total atom fitting an exact sequence controlled by the intersection matrix of vanishing cycles.
For Fourier-Mukai partners X and Y among special cubic fourfolds, t(X) ≅ t(Y), with explicit descriptions in rational and conjecturally irrational cases plus an equivariant construction for order-3 automorphisms.
Defines an interacting multi-node light-sector package for finite-node conifold degenerations of Calabi-Yau threefolds and proves a block-reduced structure theorem that isolates relation collapse and residual global sector interactions.
For special cubic fourfolds that are Fourier-Mukai partners, transcendental motives are isomorphic, with explicit descriptions in Hassett divisor families and for those with order-3 automorphisms.
This paper examines arithmetic and Hodge-theoretic properties of isomorphisms from the decomposition theorem in quantum cohomology of blowups to underpin rationality studies.
citing papers explorer
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Gamma conjecture II via global Gamma-I
Proves Gamma conjecture II for del Pezzo surfaces by establishing a global Gamma-I property that propagates from one (SR) point and relating it to non-semisimple cases.
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Quantum cohomology and birational geometry of Verra fourfolds
Verra fourfolds have a distinct small quantum cohomology ring implying they are never birational to very general cubic or Gushel-Mukai fourfolds, with primitive cohomology matching a K3 surface when birational.
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The quartic threefold is symplectically irrational
Smooth quartic threefolds are symplectically irrational, shown via an obstruction from big quantum cohomology eigenvalue multiplicities that is invariant under symplectic operations.
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Naive atoms of blowups: examples
Defines naive atomic decompositions and checks a naive version of Iritani's blowup formula in computable examples.
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Defect Triangles and Intersection-Space Hodge Atom Shadows for Calabi--Yau Conifolds
A projection of the variation morphism defines an intersection-space Hodge atom shadow package for Calabi-Yau conifolds, yielding a middle-degree IC-intersection-space defect of rank 202 for the 125-node quintic.
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Hodge Atoms at Conifold Degenerations: F-Bundles, Limiting Mixed Hodge Modules, and the Rigid-Flexible Decomposition
Constructs a canonical rigid-flexible decomposition of Hodge atoms for conifold degenerations of Calabi-Yau threefolds, with the total atom fitting an exact sequence controlled by the intersection matrix of vanishing cycles.
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Kuznetsov components ans transcendental motives of cubic fourfolds
For Fourier-Mukai partners X and Y among special cubic fourfolds, t(X) ≅ t(Y), with explicit descriptions in rational and conjecturally irrational cases plus an equivariant construction for order-3 automorphisms.
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Interacting Multi-Node Conifold Light Sectors
Defines an interacting multi-node light-sector package for finite-node conifold degenerations of Calabi-Yau threefolds and proves a block-reduced structure theorem that isolates relation collapse and residual global sector interactions.
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Kuznetsov components and transcendental motives of cubic fourfolds
For special cubic fourfolds that are Fourier-Mukai partners, transcendental motives are isomorphic, with explicit descriptions in Hassett divisor families and for those with order-3 automorphisms.
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Notes on the decomposition theorem for blowups
This paper examines arithmetic and Hodge-theoretic properties of isomorphisms from the decomposition theorem in quantum cohomology of blowups to underpin rationality studies.