Deepesh Singhal

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math.AG2026

Largest zero-dimensional intersection of $r$ degree $d$ hypersurfaces

Yuxin Lin, Deepesh Singhal

Suppose we have $r$ hypersurfaces in $P^{m}$ of degree $d$ , whose defining polynomials are linearly independent, and their intersection has dimension $0$ . Then what is the l…

math.AG2025

On a conjecture of Beelen, Datta and Ghorpade for the number of points of varieties over finite fields

Deepesh Singhal, Yuxin Lin

Consider a finite field $F_{q}$ and positive integers $d, m, r$ with $1 \leq r \leq (d m + d)$ . Let $S_{d} (m)$ be the $F_{q}$ vector space of all homogeneous polynomia…

Largest zero-dimensional intersection of r degree d hypersurfaces

On a conjecture of Beelen, Datta and Ghorpade for the number of points of varieties over finite fields

Largest zero-dimensional intersection of $r$ degree $d$ hypersurfaces