Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
de la Bretèche, Sur le nombre de points de hauteur bornée d’une certaine surface cubique singulière , Astérisque 251 (1998), 51–77 (French, with French summary)
3 Pith papers cite this work. Polarity classification is still indexing.
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Classifies irreducible components of Kontsevich moduli spaces for genus one stable maps on degree 4 and 5 del Pezzo threefolds and verifies Geometric Manin's conjecture.
Derives asymptotic count of semi-integral points on singular cubic hypersurfaces X_k and shows agreement with Manin's conjecture on a-invariant and b-invariant.
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Quasi-Classical Braverman--Kazhdan Intertwiners via Quiver Varieties
Constructs equivariant isomorphisms Φ(P,P') between affinized cotangent bundles of Braverman-Kazhdan spaces for conjugate parabolics in SL_n, satisfying Coxeter relations via SL-gauge reflection functors on type A quiver varieties.
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Moduli space of genus one curves on quartic and quintic del Pezzo threefolds
Classifies irreducible components of Kontsevich moduli spaces for genus one stable maps on degree 4 and 5 del Pezzo threefolds and verifies Geometric Manin's conjecture.
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The distribution of semi-integral points on a class of singular cubic hypersurfaces
Derives asymptotic count of semi-integral points on singular cubic hypersurfaces X_k and shows agreement with Manin's conjecture on a-invariant and b-invariant.