Related papers: On deformations of Q-Fano threefolds
We investigate some coboundary map associated to a $3$-dimensional terminal singularity which is important in the study of deformations of singular $3$-folds. We prove that this map vanishes only for quotient singularities and a…
In this article, we prove that any $\Bbb Q$-factorial weak Fano 3-fold with only terminal singularities has a smoothing.
We prove that a weak $\mathbb{Q}$-Fano $3$-fold with terminal singularities has unobstructed deformations. By using this result and computing some invariants of a terminal singularity, we provide two results on global deformation of a weak…
In this article, we prove that any Q-Calabi-Yau 3-fold with only ordinary terminal singularities and any Q-Fano 3-fold of Fano index 1 with only terminal singularities have Q-smoothings.
We study deformations of a pair of a $\mathbb{Q}$-Fano $3$-fold $X$ with only terminal singularities and its elephant $D \in |{-}K_X|$. We prove that, if there exists $D \in |{-}K_X|$ with only isolated singularities, the pair $(X,D)$ can…
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…
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…
This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general…
We study the K-stability of singular Fano 3-folds with canonical Gorenstein singularities whose anticanonical linear system is base-point-free but not very ample.
A $\mathbb Q$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of $\mathbb…
We present some applications of the deformation theory of toric Fano varieties to K-(semi/poly)stability of Fano varieties. First, we present two examples of K-polystable toric Fano 3-fold with obstructed deformations. In one case, the…
In this paper we study the deformation and Q-Gorenstein deformation theory of schemes with non-isolated singularities. We obtain obstruction spaces for the existence of deformations and also for local deformations to exist globally. Finally…
Motivated by DeVleming's work on moduli of surfaces in $\mathbb{P}^3$ and Chen-Hu-Jiang's work on moduli of threefolds with volume $2$ and geometric genus $4$, we study the deformation of pairs of $\mathbb{P}^3$ and hypersurfaces using the…
We study smoothings of Fano threefolds. We prove that the Picard number remains constant in the case of terminal Gorenstein singularities.
We study the problem of smoothing Fano and Calabi-Yau varieties with isolated Du Bois lci singularities. For Fano varieties, we show that any such $Y$ admits a deformation to a Fano variety with only $1$-rational singularities, and if none…
We propose in this article the study of the deformations of a Calabi-Yau type foliations $\mathcal{F}$. For three different types of deformations (unfoldings, holomorphic, transversally holomorphic) there exist Kuranishi spaces…
We shall prove that any small deformation of a Q-factorial projective symplectic variety with terminal singularities is locally rigid; in other words, it preserves the singularity. In particular, many singular symplectic moduli of…
We study degree of irrationality of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces that have terminal singularities.
We study the deformation theory of a Fano variety X with normal crossing singularities of dimension at most three. We obtain a formula for the sheaf T^1(X) of first order deformations of X in a suitable log resolution of X and its singular…
By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of smoothable Fano 3-folds.