20 research outputs found
Geometry of Schreieder's varieties and some elliptic and K3 moduli curves
We study the geometry of a class of -dimensional smooth projective
varieties constructed by Schreieder for their noteworthy Hodge-theoretic
properties. In particular, we realize Schreieder's surfaces as elliptic modular
surfaces and Schreieder's threefolds as one-dimensional families of Picard rank
surfaces.Comment: 28 pages. Contains arXiv:1603.0561
Chow motives associated to certain algebraic Hecke characters
Shimura and Taniyama proved that if is a potentially CM abelian variety
over a number field with CM by a field linearly disjoint from F, then
there is an algebraic Hecke character of such that
. We consider a certain converse to their result.
Namely, let be a potentially CM abelian variety appearing as a factor of
the Jacobian of a curve of the form . Fix positive
integers and such that . Under mild conditions on , we construct a Chow motive , defined over
, such that and
have the same Euler factors outside
finitely many primes.Comment: 20 page
Kodaira dimension of moduli spaces of hyperk\"ahler varieties
We study the Kodaira dimension of moduli spaces of polarized hyperk\"ahler
varieties deformation equivalent to the Hilbert scheme of points on a K3
surface or O'Grady's ten dimensional variety. This question was studied by
Gritsenko-Hulek-Sankaran in the cases of and OG10 type when the
divisibility of the polarization is one. We generalize their results to higher
dimension and divisibility. As a main result, for almost all dimensions we
provide a lower bound on the degree such that for all higher degrees, every
component of the moduli space of polarized hyperk\"ahler varieties of
type is of general type.Comment: 56 pages. Comments are welcome
On product identities and the Chow rings of holomorphic symplectic varieties
For a moduli space of stable sheaves over a surface , we propose
a series of conjectural identities in the Chow rings generalizing the classic Beauville-Voisin identity for
a surface. We emphasize consequences of the conjecture for the structure
of the tautological subring The conjecture
places all tautological classes in the lowest piece of a natural filtration
emerging on , which we also discuss. We prove the proposed
identities when is the Hilbert scheme of points on a surface.Comment: A discussion of a natural filtration on the Chow groups of M,
emerging from the paper's point of view, was adde