Related papers: On K-moduli of quartic threefolds

For a generic anti-canonical hypersurface in each smooth toric Fano 4-fold with rank 2 Picard group, we prove there exist three isolated rational curves in it. Moreover, for all these 4-folds except one, the contractions of generic…

This paper is devoted to the study of holomorphic distributions of dimension and codimension one on smooth weighted projective complete intersection Fano manifolds threedimensional, with Picard number equal to one. We study the relations…

We determine the complete list of anticanonically embedded quasi smooth log Fano 3-folds in weighted projective 4-spaces. This implies that the Reid-Fletcher list of 95 types of anticanonically embedded quasi smooth terminal Fano threefolds…

The purpose of this note is twofold. First, we give a quick proof of Ballico-Chiantini's theorem stating that a Fano or Calabi-Yau variety of dimension at least 4 in codimension two is a complete intersection. Second, we improve Barth-Van…

There exist exactly 166 4-dimensional reflexive polytopes such that the corresponding 4-dimensional Gorenstein toric Fano varieties have at worst terminal singularities in codimension 3 and their anticanonical divisor is divisible by 2. For…

Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the generic case when X is smooth and a complete intersection of…

In this article, we introduce a new approach to show the existence and smoothing of simple normal crossing varieties in a given projective space. Our approach relates the above to the existence of nowhere reduced schemes called ribbons and…

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…

Complete intersections inside rational homogeneous varieties provide interesting examples of Fano manifolds. For example, if $X = \cap_{i=1}^r D_i \subset G/P$ is a general complete intersection of $r$ ample divisors such that $K_{G/P}^*…

We describe explicitly the chamber structure of the movable cone for a general complete intersection Calabi--Yau threefold in a non-split $(n + 4)$-dimensional $\mathbb{P}^{n}$-ruled Fano manifold of index $n + 1$ and Picard number two.…

We introduce a compact moduli of noncommutative quadrics, and show that it is the weighted projective space of weight (2,4,4,6). We also introduce a compact moduli of potentials for the conifold quiver, and show that it is the weighted…

Under a hypothesis on $k$, $d$ and $n$ that is almost the best possible, we prove that for every smooth degree $d$ hypersurface in $P^n$, the $k$-plane sections dominate the moduli space of degree $d$ hypersurface in $P^k$. Using this we…

We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…

In this paper, we investigate the geometry of the orbit space of the closure of the subscheme parametrizing smooth Fano K\"ahler-Einstein manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a…

We first prove an isomorphism between the moduli space of smooth cubic threefolds and the moduli space of hyperkaehler fourfolds of K3^{[2]}-type with a non-symplectic automorphism of order three, whose invariant lattice has rank one and is…

We examine in detail the stable reduction of Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup of order p^n. If G is further assumed to be…

We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality.

We study moduli spaces of Ulrich bundles of rank $r \geq 2$ on the Fano 3-fold $V_5$ of Picard number 1, degree 5 and index 2. We prove that the moduli space of stable Ulrich bundles of rank $r$ on $V_5$ can be identified with a smooth…

We consider deformations of a toroidal orbifold $T^4/Z_2$ and an orbifold of quartic in $CP^3$. In the $T^4/Z_2$ case, we construct a family of noncommutative K3 surfaces obtained via both complex and noncommutative deformations. We do this…

We develop a framework to study the K-stability of weighted Fano hypersurfaces based on a combination of birational and convex-geometric techniques. As an application, we prove that all quasi-smooth weighted Fano hypersurfaces of index 1…