Dingxin Zhang

activity

20242026

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5 papers · 1 filter

math.AG2026

Classical and irregular Hodge numbers

Yichen Qin, Dingxin Zhang

Let $U$ be a smooth quasi-projective complex variety with a regular function $f$ . The twisted de Rham cohomology groups $H_{dR}^{k} (U, f)$ carry the decreasing irre…

math.AG2026

Asymptotic Betti bounds for hypersurfaces in a singular variety

Xuanyu Pan, Dingxin Zhang, Xiping Zhang

We show that for any degree $d$ hypersurface $Y \subset X$ in a possibly singular projective variety $X \subset P^{N}$ , the total Betti number of $Y$ is bounded by $3\text{d…

math.AG2026

Weil conjectures and affine hypersurfaces

Dingxin Zhang

We give yet another proof of the Riemann hypothesis for smooth proper varieties over a finite field (Deligne's theorem), by reducing to the hypersurface case. The latter was establ…

math.AG2025

Betti number bounds for varieties and exponential sums

Daqing Wan, Dingxin Zhang

Using basic properties of perverse sheaves, we give new upper bounds for compactly supported Betti numbers for arbitrary affine varieties in $A^{n}$ defined by $r$ polynomia…

math.AG2024

On sums of Betti numbers of affine varieties

Dingxin Zhang

We show that if V is a subvariety of the affine N-space defined by polynomials of degree at most d, then the sum of its $ℓ$ -adic Betti numbers does not exceed $2(N + 1)^{2N +1}(…