Interpolation of fat points on K3 and abelian surfaces

Adrian Zahariuc

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arXiv · 2312.12092

Interpolation of fat points on K3 and abelian surfaces

Adrian Zahariuc

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Abstract

We prove that any number of general fat points of any multiplicities impose the expected number of conditions on a linear system on a smooth projective surface, in several cases including primitive linear systems on very general K3 and abelian surfaces, `Du Val' linear systems on blowups of ${\mathbb P}^2$ at $9$ very general points, and certain linear systems on some ruled surfaces over elliptic curves. This is done by answering a question of the author about the case of only one fat point on a certain ruled surface, which follows from a circle of results due to Treibich--Verdier, Segal--Wilson, and others.

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Adrian Zahariuc. 2023-12-19. Interpolation of fat points on K3 and abelian surfaces. https://arxiv.org/abs/2312.12092

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