2022
DOI: 10.48550/arxiv.2207.12608
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Birational geometry of Beauville-Mukai systems II: general theory in low ranks

Abstract: Via wall-crossing, we study the birational geometry of Beauville-Mukai systems on K3 surfaces with Picard rank one. We show that there is a class of walls which are always present in the movable cones of Beauville-Mukai systems. We give a complete description of the birational geometry of rank two Beauville-Mukai systems when the genus of the surface is small.

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Cited by 1 publication
(3 citation statements)
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References 15 publications
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“…When k = 1, Hilb 5 (S) is birational to the Beauville-Mukai system M (0, 2, −1). Its birational geometry has been studied in [Hel20] and [QS22b]. This proves (1).…”
Section: Applications Of the Proofsupporting
confidence: 57%
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“…When k = 1, Hilb 5 (S) is birational to the Beauville-Mukai system M (0, 2, −1). Its birational geometry has been studied in [Hel20] and [QS22b]. This proves (1).…”
Section: Applications Of the Proofsupporting
confidence: 57%
“…We will call the subset of {(x, y) ∈ R 2 | y > 0} consisting of such pairs of (x, y) the xy-plane. We refer the reader to [BM14b,QS22b] for the wall and chamber structure on the xy-plane.…”
Section: Settingmentioning
confidence: 99%
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