Related papers: Correspondence scrolls
We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…
In this paper we study some properties of degenerations of surfaces whose general fibre is a smooth projective surface and whose central fibre is a reduced, connected surface $X \subset IP^r$, $r \geq 3$, which is assumed to be a union of…
The versal deformation of Stanley-Reisner schemes associated to equivelar triangulations of the torus is studied. The deformation space is defined by binomials and there is a toric smoothing component which I describe in terms of cones and…
It is known that the smooth rational threefolds of P^5 having a rational non-special surface of P^4 as general hyperplane section have degree d=3,... ,7. We study such threefolds X from the point of view of linear systems of surfaces in…
We supply a detailed proof of the result by P.S. Green and T. H$\ddot{\text{u}}$bsch that all complete intersection Calabi--Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the…
We present the first explicit examples of a rational threefold and a Calabi-Yau threefold, admitting biregular automorphisms of positive entropy not preserving any dominant rational maps to lower positive dimensional varieties. The most…
Constant cycle curves on a K3 surface $X$ over $\mathbb{C}$ have been introduced by Huybrechts (2014) as curves whose points all define the same class in the Chow group. In this paper we study correspondences $Z \subseteq X\times X$ over…
The aim of this paper is to construct families of Calabi--Yau 3-folds without boundary points with maximal unipotent monodromy and to describe the variation of their Hodge structures. In particular five families are constructed. In all…
We construct a general class of correspondences on hyperelliptic Riemann surfaces of arbitrary genus that combine finitely many Fuchsian genus zero orbifold groups and Blaschke products. As an intermediate step, we first construct analytic…
We generalize Calabi-Yau 3-folds from the special Lagrangian perspective. More precisely, we study SU(3)-structures which admit as "nice" a local special Lagrangian geometry as the flat $\mathbf{C}^3$ or a Calabi-Yau structure does. The…
We define and compute higher rank analogs of Pandharipande-Thomas stable pair invariants in primitive classes for K3 surfaces. Higher rank stable pair invariants for Calabi-Yau threefolds have been defined by Sheshmani \cite{shesh1,shesh2}…
We introduce the notion of Wall-Crossing Structure and discuss it in several examples including complex integrable systems, Donaldson-Thomas invariants and Mirror Symmetry. For a big class of non-compact Calabi-Yau 3-folds we construct…
We construct 16 new examples of Calabi--Yau threefolds with Picard group of rank 1. Each of these examples is obtained by smoothing the image of a primitive contraction with exceptional divisor being a del Pezzo surface of degree 6, 7 or…
We use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 3-folds (including all CY complete intersections in products of…
We consider a generalization of Einstein-Sasaki manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We…
We examine the structure of Farey maps, which are a class of maps (graph embeddings on surfaces) that have received significant attention recently. We describe how they are related to each other through regular coverings and parallel…
The first part of this paper discusses general procedures for finding numerical approximations to distinguished Kahler metrics, such as Calabi-Yau metrics, on complex projective manifolds. These procedures are closely related to ideas from…
We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.
We prove the following results. If $X_3$ is a generic complete intersection Calabi-Yau 3-fold, (1) then for each natural number $d$ there exists a rational map \par\hspace{1 cc} $c\in Hom_{bir}(\mathbf P^1, X_3)$ of $deg(c(\mathbf P^1))=d$,…
We describe smooth rational projective algebraic surfaces over an algebraically closed field of characteristic different from 2 which contain $n \ge \b_2-2$ disjoint smooth rational curves with self-intersection -2, where $\b_2$ is the…