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arXiv · 2501.13267

Effective non-vanishing for weighted complete intersections of low codimension

Alessandro Passantino
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Abstract

We show that on quasi-smooth weighted complete intersections of codimension at most 3, any ample Cartier divisor $H$ such that $H-K_X$ is ample admits a nontrivial global section. This is done by proving a generalisation of a numerical conjecture formulated by Pizzato, Sano and Tasin, which relates the existence of global sections of $H$ to the Frobenius number of the numerical semigroup generated by the weights of the ambient projective space.

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Alessandro Passantino. 2025-01-22. Effective non-vanishing for weighted complete intersections of low codimension. https://arxiv.org/abs/2501.13267

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