Nonsymplectic automorphisms of prime order on O'Grady's sixfolds

关于‘奥格雷迪六维流形上素数阶非辛自同构’的勘误

Corrigendum to "Nonsymplectic automorphisms of prime order on O'Grady's sixfolds"

该笔记对奥格雷迪六维流形上素数阶非辛自同构的格理论分类进行勘误，补充缺失情况及找回方法。

Monodromy and birational geometry of O'Grady's sixfolds

We prove that the bimeromorphic class of a hyperkähler manifold deformation equivalent to O'Grady's six dimensional one is determined by the Hodge structure of its Beauville-Bogomolov lattice by showing that the monodromy group is maximal. As applications, we give the structure for the Kähler and the birational Kähler cones in this deformation class and we prove that the existence of a square zero divisor implies the existence a rational lagrangian fibration with fixed fibre types.

O'Grady六维流形上的有限阶辛双有理变换

Symplectic birational transformations of finite order on O'Grady's sixfolds

本文证明了OG6型流形上的有限阶辛自同构和双有理变换分别在BBF格与判别群上作用平凡，并分类了所有可能的不变与余不变子格。

Induced birational transformations on O'Grady's sixfolds

We introduce the notion of induced birational transformations of irreducible holomorphic symplectic sixfolds of the sporadic deformation type discovered by O'Grady. We give a criterion to determine when a manifold of $OG_6$ type is birational to a moduli space of sheaves on an abelian surface. Then we determine when a birational transformation of the moduli space is induced by an automorphism of the abelian surface. Referring to the Mongardi--Rapagnetta--Saccá birational model of manifolds of $OG_6$ type, we give a result to determine when a birational transformation is induced at the quotient…