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_6501
https://research-explorer.app.ist.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/arxiv/2010.08976
info:eu-repo/grantAgreement/EC/H2020/754411
info:eu-repo/semantics/openAccess