We study log canonical thresholds (also called global log canonicalthreshold or α-invariant)
of R-linear systems. We prove existence of positive lower bounds in different settings, in …

We consider families ${\cal F}(\Delta) $ consisting of complex $(n-1) $-dimensional
projective algebraic compactifications of $\Delta $-regular affine hypersurfaces $ Z_f …

In this paper, we study the linear systems |-mK_X| on Fano varieties X with klt singularities.
In a given dimension d, we prove |-mK_X| is non-empty and contains an element with``good …

Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program
toward the biregular and/or birational classification of higher dimensional algebraic …

We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic
variety X with at worst log-terminal singularities. We prove some basic properties of stringy E …

The biregular classification of smooth d-dimensional toric Fano varieties is equivalent to the
classification of special simplicial polyhedra P in ℝ d, the so-called Fano polyhedra, up to an …

arXiv:math/0606242v4 [math.AG] 31 Oct 2007 Page 1 arXiv:math/0606242v4 [math.AG] 31
Oct 2007 TOWARDS THE SECOND MAIN THEOREM ON COMPLEMENTS YU. G …

We develop the moduli theory of boundary polarized CY pairs, which are slc Calabi-Yau
pairs $(X, D) $ such that $ D $ is ample. The motivation for studying this moduli problem is to …

We introduce machine learning methodology to the study of lattice polytopes. With
supervised learning techniques, we predict standard properties such as volume, dual …

Reflexive polyhedra encode the combinatorial data for mirror pairs of Calabi–Yau
hypersurfaces in toric varieties. We investigate the geometrical structures of circumscribed …