article published yes Tanya K Srivastava author 4D046628-F248-11E8-B48F-1D18A9856A87 TaHa department ISTplus - Postdoctoral Fellowships project 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. Elsevier2021 eng 0007-4497 2010.08976 00062388160000910.1016/j.bulsci.2021.102957 16703 Srivastava, T. K. (2021). Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. <i>Bulletin Des Sciences Mathematiques</i>. Elsevier. <a href="https://doi.org/10.1016/j.bulsci.2021.102957">https://doi.org/10.1016/j.bulsci.2021.102957</a> Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>. Elsevier, 2021. <a href="https://doi.org/10.1016/j.bulsci.2021.102957">https://doi.org/10.1016/j.bulsci.2021.102957</a>. T.K. Srivastava, Bulletin Des Sciences Mathematiques 167 (2021). Srivastava TK. 2021. Pathologies of the Hilbert scheme of points of a supersingular Enriques surface. Bulletin des Sciences Mathematiques. 167(03), 102957. 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> Srivastava, Tanya K. “Pathologies of the Hilbert Scheme of Points of a Supersingular Enriques Surface.” <i>Bulletin Des Sciences Mathematiques</i>, vol. 167, no. 03, 102957, Elsevier, 2021, doi:<a href="https://doi.org/10.1016/j.bulsci.2021.102957">10.1016/j.bulsci.2021.102957</a>. T. K. Srivastava, “Pathologies of the Hilbert scheme of points of a supersingular Enriques surface,” <i>Bulletin des Sciences Mathematiques</i>, vol. 167, no. 03. Elsevier, 2021. 91732021-02-21T23:01:20Z2025-04-14T07:43:51Z