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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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← all fields·5 papers on “vector bundles” in Differential Geometry · 1 month

The deformed Vortex equations and equivariant stability conditionsmath.DG

Study higher rank deformed Hermitian-Yang-Mills equations for stable vector bundles.

problem Stability conditions for higher rank vector bundles over complex manifolds.

method Establish equivalence between dHYM equations and

Z

-stability.

result Equivalence between dHYM solutions and

Z

-stability for vortex type bundles.

deformed Hermitian-Yang-Mills equations vector bundles stability conditions equivariant holomorphic compact Riemann surface

2026-07-20abs ↗pdf ↗

m

-Positive Stability of Holomorphic Vector Bundles and Moduli Spacesmath.DG

New stability criteria for vector bundles linked to Hermite-Einstein geometry.

problem Stability of higher-rank vector bundles and their moduli spaces.

method Introducing

m

-positivity and a smooth function for coherent subbundles, linking to Hermite-Einstein geometry.

result Hermite-Einstein bundles are uniformly semi-stable, and new stability conditions are established.

vector bundles stability Hermite-Einstein moduli spaces coherent subbundles

2026-07-19abs ↗pdf ↗

Obstructions to Deformation Quantization of Bundlesmath.AG

The paper examines obstacles to extending deformation quantization of vector bundles.

problem Obstructing the extension of deformation quantization to higher orders.

method Analyzes the obstruction class and proves its necessity and sufficiency under certain conditions.

result Establishes that extending deformation quantization to higher orders is possible under specific conditions.

Deformation Quantization Vector Bundles Obstructions Algebraic Varieties Complex Manifolds

2026-07-14abs ↗pdf ↗

Duals of higher vector bundles and cotangents of Lie 2-groupoidsmath.DG

Defines duals of higher vector bundles for Lie 2-groupoids.

problem Constructing duals for higher vector bundles over Lie 2-groupoids.

method Develops theory of n-duals for simplicial vector spaces, defines n-duals for Lie 2-groupoids, and studies their properties.

result Proposes a new construction for VB 2-duals of VB 2-groupoids, showing they are VB 2-groupoids themselves and have nondegenerate canonical dual pairings up to homotopy.

Lie 2-groupoids VB 2-groupoids cotangent symplectic duals

2026-07-13abs ↗pdf ↗

Point Singularities and Bubbling in Degenerations of Rank-Two Bundles on Threefoldsmath.DG

Degenerations of rank-two bundles on threefolds lead to isolated point singularities, with rigidity and bubbling properties.

problem Degenerations of rank-two vector bundles on complex threefolds to a rank-two torsion-free sheaf with an isolated point singularity.

method Proving a rigidity identity and using it to obtain smoothability obstructions and construct local smoothings.

result Smoothability obstructions and local smoothings are obtained, with a rigidity identity linking algebraic bubbling multiplicity and Ext-length.

rigidity bubbling smoothability threefolds vector bundles

2026-06-23abs ↗pdf ↗