15 research outputs found
Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions
In this note we construct conifold transitions between several Calabi-Yau
threefolds given by Pfaffians in weighted projective spaces and Calabi-Yau
threefolds appearing as complete intersections in toric varieties. We use the
obtained results to predict mirrors following ideas of \cite{BCKS,
Batsmalltoricdegen}. In particular we consider the family of Calabi--Yau
threefolds of degree 25 in obtained as a transverse intersection
of two Grassmannians in their Plucker embeddings.Comment: 11 pages, minor change
EPW Cubes
We construct a new 20-dimensional family of projective 6-dimensional
irreducible holomorphic symplectic manifolds. The elements of this family are
deformation equivalent with the Hilbert scheme of three points on a K3 surface
and are constructed as natural double covers of special codimension 3
subvarieties of the Grassmanian G(3,6). These codimension 3 subvarieties are
defined as Lagrangian degeneracy loci and their construction is parallel to
that of EPW sextics, we call them the EPW cubes. As a consequence we prove that
the moduli space of polarized IHS sixfolds of K3-type, Beauville-Bogomolov
degree 4 and divisibility 2 is unirational.Comment: minor corrections, 25 pages, to appear in J. Reine Angew. Mat
Fiber products of elliptic surfaces with section and associated Kummer fibrations
We investigate Calabi--Yau three folds which are small resolutions of fiber
products of elliptic surfaces with section admitting reduced fibers. We start
by the classification of all fibers that can appear on such varieties. Then, we
find formulas to compute the Hodge numbers of obtained three folds in terms of
the types of singular fibers of the elliptic surfaces. Next we study Kummer
fibrations associated to these fiber products.Comment: To appear in Internat. J. Math. 23 page
A cascade of determinantal Calabi--Yau threefolds
We study Kustin--Miller unprojections of Calabi--Yau threefolds. As an
application we work out the geometric properties of Calabi--Yau threefolds
defined as linear sections of determinantal varieties. We compute their Hodge
numbers and describe the morphisms corresponding to the faces of their
K\"{a}hler--Mori cone.Comment: corrected hodge numbers of two familie
Verra fourfolds, twisted sheaves and the last involution
We study the geometry of some moduli spaces of twisted sheaves on K3
surfaces. In particular we introduce induced automorphisms from a K3 surface on
moduli spaces of twisted sheaves on this K3 surface. As an application we prove
the unirationality of moduli spaces of irreducible holomorphic symplectic
manifolds of -type admitting non symplectic involutions with
invariant lattices or . This
complements the results obtained in [Mongardi and Wandel 2015], [Bossiere et al
2016], and the results from [arXiv:1603.00403] about the geometry of IHS
fourfolds constructed using the Hilbert scheme of conics on Verra
fourfolds. As a byproduct we find that IHS fourfolds of -type with
Picard lattice naturally contain non-nodal Enriques
surfaces.Comment: 36 pages; comments are welcome. Sections 2.3 and 3 slightly revised;
Proposition 6.14, statement and proof modifie