Related papers: On Quasismooth Weighted Complete Intersections
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
Our main theorem characterizes the complete intersections of codimension 2 in a projective space of dimension 3 or more over an algebraically closed field of characteristic 0 as the subcanonical and self-linked subschemes. In order to prove…
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
We provide new logarithmic lower bounds for the torsion order of a very general complete intersection in projective space as well as a very general hypersurface in products of projective spaces and Grassmannians, in particular we prove…
We present a generalization of the complete intersection in products of projective space (CICY) construction of Calabi-Yau manifolds. CICY three-folds and four-folds have been studied extensively in the physics literature. Their utility…
Euler-symmetric projective varieties, introduced by Baohua Fu and Jun-Muk Hwang in 2020, are nondegenerate projective varieties admitting many $\mathbb{C}^{\times}$-actions of Euler type. They are quasi-homogeneous and uniquely determined…
We establish a weighted version of the $H^p$-theory of quasiconformal mappings.
We obtain all linear Chern number inequalities satisfied by any smooth complete intersection threefold with ample canonical bundle.
We prove that one can realize certain triangulated subcategories of the singularity category of a complete intersection as homotopy categories of matrix factorizations. Moreover, we prove that for any commutative ring and non-zerodivisor,…
We construct a family of canonical connections and surrounding basic theory for almost complex manifolds that are equipped with an affine connection. This framework provides a uniform approach to treating a range of geometries. In…
We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent…
Given a smooth subscheme of a projective space over a finite field, we compute the probability that its intersection with a fixed number of hypersurface sections of large degree is smooth of the expected dimension. This generalizes the case…
The aim of this paper is to classify indecomposable rank 2 arithmetically Cohen-Macaulay (ACM) bundles on compete intersection Calabi-Yau (CICY) threefolds and prove the existence of some of them. New geometric properties of the curves…
Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This…
Let $M_1$ and $M_2$ be closed connected orientable $3$-manifolds. We classify the sets of smooth and piecewise linear isotopy classes of embeddings $M_1\sqcup M_2\rightarrow S^6$.
To a hyperbolic manifold one can associate a canonical projective structure and ask whether it can be deformed or not. In a cusped manifold, one can ask about the existence of deformations that are trivial on the boundary. We prove that if…
In this note we observe that Arnold conjecture for the Hamiltonian maps still holds on weighted projective spaces $\CP^n({\bf q})$, and that Arnold conjecture for the Lagrange intersections for $(\CP^n({\bf q}), \RP^n({\bf q}))$ is also…
In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This…
We prove that equivariant, holomorphic embeddings of Hermitian symmetric spaces are totally geodesic (when the image is not of exceptional type).
This work deals with the study of embeddings of toric Calabi-Yau fourfolds which are complex cones over the smooth Fano threefolds. In particular, we focus on finding various embeddings of Fano threefolds inside other Fano threefolds and…