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- Title
On Morin Configurations of Higher Length.
- Authors
Kapustka, Grzegorz; Verra, Alessandro
- Abstract
This paper studies finite Morin configurations |$F$| of planes in |$\mathbb P^5$| having higher length—a question naturally related to the theory of Gushel–Mukai varieties. The uniqueness of the configuration of maximal cardinality |$20$| is proven. This is related to the canonical genus |$6$| curve |$C_{\ell }$| union of the |$10$| lines in a smooth quintic Del Pezzo surface |$Y$| in |$\mathbb P^5$| and to the Petersen graph. More in general an irreducible family of special configurations of length |$\geq 11$| , we name as Morin–Del Pezzo configurations, is considered and studied. This includes the configuration of maximal cardinality and families of configurations of lenght |$\geq 16$| , previously unknown. It depends on |$9$| moduli and is defined via the family of nodal and rational canonical curves of |$Y$|. The special relations between Morin–Del Pezzo configurations and the geometry of special threefolds, like the Igusa quartic or its dual Segre primal, are focused.
- Subjects
PETERSEN graphs; CONFIGURATIONS (Geometry); MORIN
- Publication
IMRN: International Mathematics Research Notices, 2022, Vol 2022, Issue 1, p727
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnaa170