Pathologies of the Hilbert scheme of points of a supersingular Enriques surface Srivastava, Tanya K We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number h2,0 > 1, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over C as given by Beauville-Bogolomov decomposition theorem. Elsevier 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/9173 Srivastava TK. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. <i>Bulletin des Sciences Mathematiques</i>. 2021;167(03). doi:<a href="https://doi.org/10.1016/j.bulsci.2021.102957">10.1016/j.bulsci.2021.102957</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.bulsci.2021.102957 info:eu-repo/semantics/altIdentifier/issn/0007-4497 info:eu-repo/semantics/altIdentifier/wos/000623881600009 info:eu-repo/semantics/altIdentifier/arxiv/2010.08976 info:eu-repo/semantics/openAccess