Pathologies of Hilbert scheme of points of supersingular Enriques\n surface

2020/10/18 by Tanya Kaushal Srivastava, Srivastava, Tanya Kaushal
Computer Science · Mathematics · #14G17 #14J10 #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2010.08976

openalex publication_date 2020/10/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We show that Hilbert schemes of points on supersingular Enriques surface in\ncharacteristic 2 are simply connected, symplectic varieties but are not\nirreducible symplectic as the hodge number h^2,0 > 1, even though a\nsupersingular Enriques surface is an irreducible symplectic variety. These are\nthe classes of varieties which appear only in characteristic 2 and they show\nthat the hodge number formula for G "ottsche-Soergel does not hold over\ncharacteristic 2. It also gives examples of varieties with trivial canonical\nclass which are neither irreducible symplectic nor Calabi-Yau, thereby showing\nthat there are strictly more classes of simply connected varieties with trivial\ncanonical class in characteristic 2 than over \ℂ as given by\nBeauville-Bogolomov decomposition theorem.\n

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