Related papers: Mori Fibrations in Mixed Characteristic
We consider Scherk-Schwarz compactifications of M-theory (toroidal compactifications with a non-trivial spin structure) in various dimensions and find isolated critical points of the potential on the moduli space. We demonstrate this by…
In this paper we first note a result of birational automorphisms with bounded degree of projective varieties related with the Zariski dense orbit conjecture (ZDO) and the Zariski density of periodic points. Next, we give a reduced result of…
We introduce modular inequalities for complements of plane curves, based on a Combinatorial Aomoto complex construction associated with the weak combinatorial type of a curve. We use this as a tool to investigate twisted Alexander…
In this paper, we study the theory of complements, introduced by Shokurov, for Calabi-Yau type varieties with the coefficient set $[0,1]$. We show that there exists a finite set of positive integers $\mathcal{N}$, such that if a threefold…
We analyze a finite element/boundary element procedure to solve a non-convex contact problem for the double-well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of facets of any contracted pseudotriangulation of a connected closed 3-manifold…
This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…
This paper identifies a new class of shape invariant models. These models are based on extensions of conventional quantum mechanics that satisfy a string-motivated minimal length uncertainty relation. An important feature of our…
The Gromov-Witten theory of threefolds admitting a smooth K3 fibration can be solved in terms of the Noether-Lefschetz intersection numbers of the fibration and the reduced invariants of a K3 surface. Toward a generalization of this result…
We give a sufficient condition for the termination of flips. Then we discuss a semi-stable minimal model program for varieties with (numerically) trivial canonical divisor as an application. We also treat a slight refinement of dlt…
For a K3 surface S, we study motivic invariants of stable pairs moduli spaces associated to 3-fold thickenings of S. We conjecture suitable deformation and divisibility invariances for the Betti realization. Our conjectures, together with…
This paper analyse the properties of minimal solutions for the reconstruction of the lens potential in the singular perturbative approach. These minimal solutions corresponds to an expansion with a minimal degree in Fourier expansion of the…
This paper considers submodular function minimization (SFM) restricted to a family of subsets. We show that SFM over complements of families with certain hierarchical structures can be solved in polynomial-time. This yields a…
We prove the normality of minimal log canonical centers on threefold pairs which residue fields are perfect of residue characteristics $p\neq 2,3 $ and $5$. We also show that the union of all log canonical centers on threefold pairs with…
We consider a coset construction of minimal models. We define it rigorously and prove that it gives superconformal minimal models. This construction allows to build all primary fields of superconformal models and to calculate their…
We investigate the combinatorial analogues, in the context of normal surfaces, of taut and transversely measured (codimension 1) foliations of 3-manifolds. We establish that the existence of certain combinatorial structures, a priori weaker…
Let X be a compact K\"ahler threefold that is not uniruled. We prove that X has a minimal model.
In this article, we consider minimal $L^2$ integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K\"ahler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and…
This paper develops mixed-normal approximations for probabilities that vectors of multiple Skorohod integrals belong to random convex polytopes when the dimensions of the vectors possibly diverge to infinity. We apply the developed theory…