相关论文: Addendum/Erratum to the paper "Weyl groups and Bir…
We complete the analysis on the birational rigidity of quasismooth Fano 3-fold deformation families appearing in the Graded Ring Database as a complete intersection. When such a deformation family $X$ has Fano index at least 2 and is…
We characterize the birational geometry of some hyperk\"ahler fourfolds of Picard rank $3$ obtained as the Fano varieties of lines on cubic fourfolds containing pairs of cubic scrolls. In each of the two cases considered, we identify all of…
We find all $P$-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces Jan Steven's list [Manuscripta Math. 1993] of the numbers…
In this paper, a procedure is developed to construct compact F-theory fourfolds corresponding to perturbative IIB O7/O3 models on CICY threefolds with permutation involutions. The method is explained in generality, and then applied to…
Building on the work of Casagrande-Codogni-Fanelli, we develop our study on the birational geometry of the Fano fourfold $Y=M_{S,-K_S}$ which is the moduli space of semi-stable rank-two torsion-free sheaves with $c_1=-K_S$ and $c_2=2$ on a…
Building on the work of Mukai, we explore the birational geometry of the moduli spaces M_{S,L} of semistable rank two torsion-free sheaves, with c_1=-K_S and c_2=2, on a polarized degree one del Pezzo surface (S,L); this is related to the…
We study threefolds of general type constructed as $\mathbb{Z}_2^s$-covers of weighted projective spaces with a particular focus on their invariants, deformation theory, and the behavior of the $m$-canonical map. For the invariants, we…
This note continues our previous work on special secant defective (specifically, conic connected and local quadratic entry locus) and dual defective manifolds. These are now well understood, except for the prime Fano ones. Here we add a few…
In order to establish Fredholm theory on stratified topological Banach manifolds in Gromov-Witten theory, we have introduced flat structures on such manifolds in [L4]. Such a structure is obtained from local flat coordinate charts. The…
This paper is a continuation of our first paper [10] in which we showed how deformation theory of representation varieties can be used to study finite simple quotients of triangle groups. While in Part I, we mainly used deformations of the…
Varieties fibered into del Pezzo surfaces form a class of possible outputs of the minimal model program. It is known that del Pezzo fibrations of degrees $1$ and $2$ over the projective line with smooth total space satisfying the so-called…
The goal of this paper is to generalize results concerning the deformation theory of Calabi-Yau and Fano threefolds with isolated hypersurface singularites, due to the first author, Namikawa and Steenbrink. In particular, under the…
We show that mixed-characteristic and equi-characteristic small deformations of 3-dimensional canonical (resp. terminal) singularities with perfect residue field of characteristic $p>5$ are canonical (resp. terminal). We discuss…
In this paper we connect degenerations of Fano threefolds by projections. Using Mirror Symmetry we transfer these connections to the side of Landau--Ginzburg models. Based on that we suggest a generalization of Kawamata's categorical…
We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four dimensional supersymmetric field theory…
We refine the classification of weak Fano threefolds with sextic del Pezzo fibrations by considering the Hodge numbers of them. By the refined classification result, such threefolds are classified into 17 cases. The main result of this…
We classify all 1-nodal degenerations of smooth Fano threefolds with Picard number 1 (both nonfactorial and factorial) and describe their geometry. In particular, we describe a relation between such degenerations and smooth Fano threefolds…
Developing on the ideas of R. Stora and coworkers, a formulation of two dimensional field theory endowed with extended conformal symmetry is given, which is based on deformation theory of holomorphic and Hermitian spaces. The geometric…
We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane-tilings and Chern-Simons theory on M2-branes probing…
Consider a family of Fano varieties $\pi: X \longrightarrow B\ni o$ over a curve germ with a smooth total space $X$. Assume that the generic fiber is smooth and the special fiber $F=\pi^{-1}(o)$ has simple normal crossings. Then $F$ is…