arXiv subjects

Enhao Feng

Publications and source records attributed to Enhao Feng.

6 recordsLinked to original sources

arXiv2026

Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces

We prove uniform exponential bounds for the compactly supported Betti numbers of spaces of morphisms from curves of fixed genus to projective varieties. For targets in a fixed projective space cut out by a prescribed number of equations of fixed degrees, the bound is exponential in the degree of the morphism and is independent of the ground field, the source curve, and the target. The proof constructs bounded-degree affine presentations involving only linearly many variables and equations, and then applies Katz's estimate. As an application, we establish a higher genus function field version of Manin's conjecture for split quartic del Pezzo surfaces, generalizing a recent theorem of Das--Lehmann--Tanimoto--Tosteson. Over sufficiently large finite fields, and after restricting curve classes to a slightly shrunken nef cone, we obtain the predicted asymptotic with the expected leading constant. As in Das--Lehmann--Tanimoto--Tosteson's argument, we combine the uniform Betti bound with a higher genus homological sieve, a bar complex calculation, and a virtual height zeta function.

math.AG↗

arXiv2026

Moduli space of genus one curves on quartic and quintic del Pezzo threefolds

In this article, we study the space of smooth genus one curves on del Pezzo threefolds of degree 4 and 5. We describe the irreducible components of the Kontsevich moduli space generically parametrizing genus one stable maps with irreducible domains and classify the irreducible components of the morphism space from general elliptic curves. Our result verifies the Geometric Manin's conjecture for all del Pezzo threefolds of degree 4 and 5 over the complex numbers.

math.AG↗

arXiv2026

Revealing a Systematic High-latitude Current Sheet at Jupiter

Based on models derived from Earth's magnetotail, other planets with dipole magnetic fields, including Mercury, Jupiter, and Saturn, were expected to possess similar magnetotail configurations. In this traditional picture, the majority of plasma is confined near the magnetic equator within a plasma sheet (or plasma disc), whereas higher-latitude regions feature strong magnetic fields that are open to the solar wind, forming magnetospheric lobes. However, auroral observations and recent simulations have shown that Jupiter's magnetic topology differs markedly from this picture, particularly in its high-latitude regions where magnetic field lines are predominantly closed. This discrepancy calls for a re-examination of high-latitude magnetospheric structure at Jupiter. Here, using Juno measurements acquired between 2016 and 2022, we show that Jupiter's nightside high latitudes host a persistent current-sheet-like structure above about 40 degrees magnetic latitude near midnight. This structure contains internally sourced oxygen and sulfur ions and exhibits azimuthal magnetic signatures opposite to the bend-back of the equatorial current sheet. These findings indicate that the canonical picture of planetary magnetotail architecture requires revision. Our results provide new insight into the architecture of rapidly rotating magnetospheres and offer a framework for interpreting magnetospheric structures at exoplanets.

astro-ph.EP↗

arXiv2026

GAMERA-OP: A three-dimensional finite-volume MHD solver for orthogonal curvilinear geometries

We present GAMERA-OP (Orthogonal-Plus), a three-dimensional finite-volume magnetohydrodynamics (MHD) solver for orthogonal curvilinear geometries. The solver advances magnetic fields using constrained transport to preserve $\nabla\!\cdot\!\mathbf{B}=0$ to machine precision and employs geometry-consistent high-order reconstruction with an enhanced Partial Donor Cell method (e-PDM) that accounts for geometry curvature. Flexible numerics include various numerical fluxes and time integrators. In axial symmetric coordinates, angular momentum are preserved to round-off, and a ring-averaging treatment near the axis relaxes CFL constraints while maintaining divergence-free magnetic fields. Optional capabilities include the semi-relativistic (Boris) correction, background-field splitting, and an anisotropic MHD formulation. Rewritten in C, the code adopts a modular design that simplifies case setup and facilitates the addition of physics modules and coupling to other first-principles codes. Standard benchmarks across multiple geometries verify the code's high accuracy, low numerical diffusion, and robust handling of coordinate singularities and rotating flows. GAMERA-OP provides a practical, high-order framework for space and astrophysical plasma applications where orthogonal curvilinear coordinates and exact angular-momentum conservation are advantageous.

astro-ph.IM↗

arXiv2025

Campana separable rational connectedness of toric orbifold

We prove that smooth non-klt toric orbifolds are separably Campana rationally connected, extending the result in the klt case. We also show that there always exists a positive characteristic in which a singular weighted projective space, viewed as a non-klt Campana orbifold, is not separably Campana rationally connected.

math.AG↗

arXiv2025

Moduli space of genus one curves on cubic threefold

Let $X$ be a smooth cubic threefold. By invoking ideas from Geometric Manin's Conjecture, we give a complete description of the main components of the Kontsevich moduli space of genus one stable maps $\overline{M}_{1,0}(X)$. In particular, we show that for degree $e\geqslant 5$, there are exactly two irreducible main components, of which one generically parametrizes free curves birational onto their images, and the other corresponds to degree $e$ covers of lines. As a corollary, we classify components of the morphism space $\text{Mor}(E,X)$ for a general smooth genus one curve $E$.

math.AG↗