arXiv subjects

Yonghong Huang

Publications and source records attributed to Yonghong Huang.

5 recordsLinked to original sources

arXiv2025

From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes

Using orbifold Hilbert schemes, we compactify all two-dimensional Hitchin systems corresponding to types A0-tilde, D4-tilde, E6-tilde, E7-tilde, and E8-tilde, thereby obtaining four rational elliptic surfaces with C*-actions. Their singular fibers and relative minimal models are listed in the main table. A particularly interesting point is that we found they can all be obtained by performing a finite number of blow-ups on the second Hirzebruch surface. To this end, we prove that Hilbert schemes of orbifold surfaces are connected smooth projective schemes under suitable conditions, and we use the Hilbert-Chow morphism to construct the minimal resolutions of the coarse moduli spaces.

math.AG↗

arXiv2023

Mirror symmetry and Hitchin systems on DM curves: SYZ Duality

We generalize the classical theory of Higgs bundles, spectral curves and Norm maps to Deligne-Mumford curves. As an application, under some mild conditions, we prove the Strominger-Yau-Zaslow duality for the moduli spaces of Higgs bundles over a hyperbolic stacky curve.

math.AG↗

arXiv2022

Langton's type Theorem on Algebraic Orbifolds

In this paper, we show Langton's type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k

math.AG↗

arXiv2020

Non-Embedding Theorems of Nilpotent Lie groups and Sub-Riemannian Manifolds

We prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the RCD(0,N), with N > 1. In fact, we can prove that a subRiemannian manifold whose generic degree of nonholonomy is not smaller than 2 can not be biLipschitzly embedded in any Banach space with the Radon-Nikodym property. We also get that every regular sub-Riemannian manifold do not satisfy the CD(K,N) with N > 1. We also prove that the subRiemannian manifold is infinitesimally Hilbert space.

math.DG↗

arXiv2019

Malware Evasion Attack and Defense

Machine learning (ML) classifiers are vulnerable to adversarial examples. An adversarial example is an input sample which is slightly modified to induce misclassification in an ML classifier. In this work, we investigate white-box and grey-box evasion attacks to an ML-based malware detector and conduct performance evaluations in a real-world setting. We compare the defense approaches in mitigating the attacks. We propose a framework for deploying grey-box and black-box attacks to malware detection systems.

cs.CR↗