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arXiv · 2604.27688

Towards Bigness equivalence

F. Laytimi·D. S. Nagaraj
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Abstract

On the flag variety $ \mathcal{F}l_s(E)$ associated to a vector bundle $E,$ , a sequence $s$ and a partition $a,$ there is a line bundle $\it Q^a_s$ on $ \mathcal{F}l_s(E).$ The aim of this paper is to prove the following conjecture: $Q^a_s $ on $ \mathcal{F}l_s(E)$ is big if only if $\pi_*(Q^a_s)=S_a(E)$ on X is big. The "if" part is proven here, the "only if" part is proven under the V-bigness hypothesis.

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F. Laytimi, D. S. Nagaraj. 2026-04-30. Towards Bigness equivalence. https://arxiv.org/abs/2604.27688

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