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arXiv · 2406.20008

K-moduli of log del Pezzo pairs and variations of GIT

Jesus Martinez-Garcia·Theodoros Stylianos Papazachariou·Junyan Zhao
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Abstract

We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree $d$ and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, providing a natural problem in variations of K-moduli spaces. For degrees 2, 3, 4, we establish an isomorphism between the K-moduli spaces and variations of Geometric Invariant Theory compactifications, which generalizes the isomorphisms in the absolute cases established by Odaka--Spotti--Sun and Mabuchi--Mukai.

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Jesus Martinez-Garcia, Theodoros Stylianos Papazachariou, Junyan Zhao. 2024-06-28. K-moduli of log del Pezzo pairs and variations of GIT. https://arxiv.org/abs/2406.20008

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