On the geometry of singular EPW cubes
Francesca Rizzo
TL;DR
This paper studies the geometric structure of singular EPW cubes, a family of hyper-K"ahler varieties, and constructs a smooth resolution of their singularities, enhancing understanding of their geometry.
Contribution
It provides a construction of a smooth small resolution for singular EPW cubes, extending methods used for double EPW sextics to this new class.
Findings
Construction of a smooth small resolution for singular EPW cubes
Identification of similarities between EPW cubes and double EPW sextics
Advancement in understanding the geometry of hyper-K"ahler varieties
Abstract
EPW cubes form a locally complete family of smooth projective hyper-K\"ahler varieties of dimension 6, constructed by Iliev--Kapustka--Kapustka--Ranestad.\ Their construction and behavior share a lot of similarities with the double EPW sextics constructed by O'Grady.\ Adapting the methods of O'Grady, we construct a projective smooth small resolution of singular EPW cubes.
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Taxonomy
TopicsAdvanced Antenna and Metasurface Technologies · Nonlinear Photonic Systems · Semiconductor Lasers and Optical Devices