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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.

168,742 papers · 148 categories

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6 results for “Hirzebruch-Riemann-Roch”

Some remarks on the Schweitzer complexmath.AG

We prove properties of the Schweitzer complex and its cohomologies.

problem Properties of the Schweitzer complex and its cohomologies.

method Elliptic complex and cohomological functors.

result Finite dimensionality and equivalence to Hirzebruch-Riemann-Roch relations.

Schweitzer complex cohomological functors elliptic complex finite dimensionality Serre duality

2022-04-12abs ↗pdf ↗

Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifoldsmath.DG

Develops virtual Morse-Bott indices for four-manifolds, proving inequalities.

problem Proving inequalities for four-manifolds of Seiberg-Witten simple type.

method Uses virtual Morse-Bott indices and Hirzebruch-Riemann-Roch Theorem.

result Proves positivity of virtual Morse-Bott indices, leading to inequalities.

Four-manifolds Seiberg-Witten Bogomolov-Miyaoka-Yau Hirzebruch-Riemann-Roch Monopoles

2020-10-29abs ↗pdf ↗

Yang-Mills energy quantization over non-collapsed degenerating Einstein manifolds and applicationsmath.DG

Study quantizes topological numbers on degenerating Einstein manifolds.

problem Quantizing topological numbers on non-collapsed degenerating Einstein manifolds.

method Compactness theory of bubbles, classical vanishing theorems, and Hirzebruch-Riemann-Roch theorems.

result Established quantization results for various topological numbers.

Yang-Mills connections Einstein manifolds quantization topological numbers compactness theory

2025-12-22abs ↗pdf ↗

Spectral bundles on Abelian varieties, complex projective spaces and Grassmanniansmath.DG

The paper studies spectral analysis on complex spaces and finds explicit formulas for eigensections.

problem Understanding eigensections on complex projective spaces and Grassmannians.

method Using creation and annihilation operators, converting higher energy eigensections to lower energy holomorphic sections.

result Explicit formulas for the dimension of higher-level eigensections on

\mathbb{P}^{n}

spectral analysis Abelian varieties complex projective spaces Grassmannians holomorphic sections

2025-07-19abs ↗pdf ↗

Heat kernel and local index theorem for open complex manifolds with

\mathbb{C}^{\ast }

-actionmath.DG

The paper develops a local index formula for complex manifolds with $\mathbb{C}^{\ast }$ -action.

problem Analyzing the

m

-index on complex manifolds with

\mathbb{C}^{\ast }

-action.

method Applying the method of transversal heat kernel asymptotics.

result Obtained a local index formula for the

m

-index.

Heat kernel Local index theorem Complex manifolds Cohomology Fourier-Dolbeault

2024-12-15abs ↗pdf ↗

Heat kernel asymptotics, local index theorem and trace integrals for CR manifolds with

S^1

actionmath.DG

Among those transversally elliptic operators initiated by Atiyah and Singer, Kohn's $\Box_b$ operator on CR manifolds with $S^1$ action is a natural one of geometric significance for complex analysts. Our first main result establishes an asymptotic expansion for the heat kernel of such an operator with values in its Fo…

2015-10-31abs ↗pdf ↗