M. Dolezálek

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20232026

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math.NT2025

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields

Matěj Doležálek

There exist numerous results in the literature proving that within certain families of totally real number fields, the minimal rank of a universal quadratic lattice over such a fie…

math.AG2025

Secant varieties of Segre-Veronese varieties $P^{m} \times P^{n}$ embedded by $O (1, 2)$ are non-defective for $n ≫ m^{3}$ , $m \geq 3$

Matěj Doležálek, Nikhil Ken

We prove that for any $m \geq 3$ , $n ≫ m^{3}$ , all secant varieties of the Segre-Veronese variety $P^{m} \times P^{n}$ have the expected dimension. This was already proved…

Extending bounds on minimal ranks of universal quadratic lattices to larger number fields

Secant varieties of Segre-Veronese varieties Pm×Pn embedded by O(1,2) are non-defective for n≫m3, m≥3

Secant varieties of Segre-Veronese varieties $P^{m} \times P^{n}$ embedded by $O (1, 2)$ are non-defective for $n ≫ m^{3}$ , $m \geq 3$