2024/06/28 by Jesus Martinez‐Garcia, Theodoros Stylianos Papazachariou, Martinez-Garcia, Jesus +3
Mathematics · #Algebraic Geometry (math.AG) #Approximation Theory and Sequence Spaces #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2406.20008
openalex publication_date 2024/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.