Related papers: Embedding non-projective Mori Dream Spaces

We apply computations of twisted Hodge diamonds to construct an infinite number of non-Fourier-Mukai functors with well behaved target and source spaces. To accomplish this we first study the characteristic morphism in order to control it…

Let $\text{X}$ denote a projective variety over an algebraically closed field on which a linear algebraic group acts with finitely many orbits. Then, a conjecture of Soergel and Lunts in the setting of Koszul duality and Langlands'…

We give further evidence that genus-one fibers with multi-sections are mirror dual to fibers with Mordell-Weil torsion. In the physics of F-theory compactifications this implies a relation between models with a non-simply connected gauge…

In chapter 1 we define period mappings of Hodge-de Rahm type for certain submersive, yet not necessarily locally topologically trivial, morphisms of complex manifolds. Generalizing Griffiths's theory, we interpret the differential of such…

Gotzmann's persistence theorem provides a method for determining the Hilbert polynomial of a subscheme of projective space by evaluating the Hilbert function at only two points, irrespective of the dimension of the ambient space. In…

This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…

Let $X$ be a union of a sequence of symplectic manifolds of increasing dimension and let $M$ be a manifold with a closed $2$-form $\omega$. We use Tischler's elementary method for constructing symplectic embeddings in complex projective…

Motivated by the problem of classifying toric $2$-Fano manifolds, we introduce a new invariant for smooth projective toric varieties, the minimal projective bundle dimension. This invariant $m(X)\in\{1, \dots,\dim(X)\}$ captures the minimal…

Weighted projective spaces are natural generalizations of projective spaces with a rich structure. Projective Reed-Muller codes are error-correcting codes that played an important role in reliably transmitting information on digital…

If in a given rank $r$, there is an irreducible complex local system with torsion determinant and quasi-unipotent monodromies at infinity on a smooth quasi-projective variety, then for every prime number $\ell$, there is an absolutely…

Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from an ergodic action of a finite closed subgroup of the torus, which are meant as finite dimensional approximations of…

Using the notion of a valuation into the semifield of piecewise linear functions, we give a classification of torus equivariant flat families of finite type over a toric variety base, by certain piecewise linear maps between fans. As a…

Inspired by the Weak Lefschetz Principle, we study when a smooth projective variety fully determines the birational geometry of some of its subvarieties. In particular, we consider the natural embedding of the space of complete quadrics…

Global F-theory compactifications whose fibers are realized as complete intersections form a richer set of models than just hypersurfaces. The detailed study of the physics associated with such geometries depends crucially on being able to…

We study the structure of the Mordell--Weil groups of semiabelian varieties over large algebraic extensions of a finitely generated field of characteristic zero. We consider two types of algebraic extensions in this paper; one is of…

We consider isometric immersions of complete connected Riemannian manifolds into space forms of nonzero constant curvature. We prove that if such an immersion is compact and has semi-definite second fundamental form, then it is an embedding…

We study the Cox rings of smooth anticanonical Calabi-Yau hypersurfaces in smooth toric Fano varieties. Using the combinatorics of primitive pairs of the ambient Fano polytope and the description of Cox rings of embedded varieties via…

We show that Shavel type surfaces are fake quadrics of even type which are not Mori dream surfaces, yet there are infinitely many primes $p$ such that the reduction modulo $p$ is a Mori dream surface. We investigate fake quadrics, first…

A fake weighted projective space X is a Q-factorial toric variety with Picard number one. As with weighted projective space, X comes equipped with a set of weights (\lambda_0,...,\lambda_n). We see how the singularities of…

It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…