@article{9173, abstract = {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.}, author = {Srivastava, Tanya K}, issn = {0007-4497}, journal = {Bulletin des Sciences Mathematiques}, number = {03}, publisher = {Elsevier}, title = {{Pathologies of the Hilbert scheme of points of a supersingular Enriques surface}}, doi = {10.1016/j.bulsci.2021.102957}, volume = {167}, year = {2021}, }