We perform a systematic study of Gushel-Mukai varieties-quadratic sections of linear sections of cones over the Grassmannian Gr(2, 5). This class of varieties includes Clifford general curves of genus 6, Brill-Noether general polarized K3 surfaces of genus 6, prime Fano threefolds of genus 6, and their higher-dimensional analogues.We establish an intrinsic characterization of normal Gushel-Mukai varieties in terms of their excess conormal sheaves, which leads to a new proof of the classification theorem of Gushel and Mukai. We give a description of isomorphism classes of Gushel-Mukai varieties and their automorphism groups in terms of linear-algebraic data naturally associated with these varieties.We carefully develop the relation between Gushel-Mukai varieties and EisenbudPopescu-Walter (EPW) sextics introduced earlier by Iliev-Manivel and O'Grady. We describe explicitly all Gushel-Mukai varieties whose associated EPW sextics are isomorphic or dual (we call them period partners or dual varieties, respectively). Finally, we show that in dimension 3 and higher, period partners or dual varieties are always birationally isomorphic.
The application of the multifractal parameterization method for comparing structural changes observed in an optical microscope on steel St.3 subjected to severe plastic deformation and high-rate superplastic deformation is investigated.
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