Pinxian Bie

collaborators

6 papers

math.AG2026

Sharp anticanonical volume bounds for Gorenstein Fano fourfold of Picard number one

Pinxian Bie, Zhengjie Yu

Let $X$ be a complex $Q$ -factorial Gorenstein Fano fourfold with $ρ (X) = 1$ . If $X$ has canonical singularities, we prove that $(- K_{X})^{4} \leq 3528$ , with equality if and only if…

physics.optics2026

Electromagnetically Transmissive and Thermally Opaque Engineered Microwave Interconnect

Md. Jawad Ul Islam, Ishrat Jahan, Abdelrahman Omar +3

In a standard two-conductor microwave transmission line, both the signal trace and the wide ground plane act as parasitic heat leakage paths along the propagation direction. To pre…

math.AG2026

Sharp Volume Bounds in Picard Rank One and Polynomial Bounds for Log Calabi-Yau Surfaces

Pinxian Bie

For a complex $ε$ -log canonical Fano surface of Picard number one, we prove that the anticanonical volume is at least $ε^{2} /100$ and that every integral nef and…

math.AG2026

Sharp Quadratic Bounds for Anticanonical Volumes of Weak Fano Surfaces

Pinxian Bie

We prove an explicit lower bound of optimal quadratic order for the anticanonical volume of every complex $ε$ -log canonical weak del Pezzo surface, with no restriction on its Picar…

math.AG2026

On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs

Pinxian Bie

We investigate the DCC property of the set of Iitaka volumes of a given set of pairs of varieties. We both generalize previous results of Birkar and Li about usual pairs to the rea…

math.AG2025

Explicit Effective Birationality for Singular Surfaces

Pinxian Bie

We give some explicit upper bounds on the effective birationality of the canonical or anti-canonical system for a singular surface. In particular, we show that for any surface $X$ …