Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
Hartshorne, Algebraic Geometry , Grad.\ Texts in Math., vol
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Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
A new extension-based construction produces strictly asymptotically Z-stable rank 3 bundles on polycyclic projective surfaces, plus a Hoppe-style criterion for rank 2 bundles.
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
A necessary and sufficient condition is established for the existence of holomorphic Lie algebroid connections on vector bundles over irreducible smooth complex projective varieties of dimension at least three.
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
New proof of Green's conjecture for generic odd-genus curves by adapting the author's earlier secant bundle methods to avoid difficult computations.
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Copositive Matrices with Ordered Off-Diagonal Entries
Copositive matrices with nondecreasing off-diagonal entries admit a PSD plus nonnegative decomposition, which implies exactness of a natural relaxation for separable quadratic optimization over the simplex.
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Graphical Algebraic Geometry: From Ideals and Varieties to Quantum Calculi
Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
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Asymptotically Z-stable bundles over projective surfaces
A new extension-based construction produces strictly asymptotically Z-stable rank 3 bundles on polycyclic projective surfaces, plus a Hoppe-style criterion for rank 2 bundles.
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Solvable Descent and the Grunwald Problem for Solvable Groups
A new fibration theorem implies solvable descent, solving the Grunwald problem for solvable groups up to the Brauer-Manin obstruction.
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Existence of holomorphic Lie algebroid connections in higher dimensions
A necessary and sufficient condition is established for the existence of holomorphic Lie algebroid connections on vector bundles over irreducible smooth complex projective varieties of dimension at least three.
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The Sharp Edges of Calabi-Yau Manifolds: Designing Symmetric Models for Ricci-flat Metrics
Surveys Calabi-Yau literature and symmetries, characterizes isometries, introduces volume ratio formula on CICYs, and proposes symmetry-aware GNN model for Ricci-flat metrics.
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A proof of generic Green's conjecture in odd genus
New proof of Green's conjecture for generic odd-genus curves by adapting the author's earlier secant bundle methods to avoid difficult computations.