Related papers: Virtual global generation in higher dimensions

The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…

Scalable Vector Graphics (SVG) has become the de facto standard for vector graphics in digital design, offering resolution independence and precise control over individual elements. Despite their advantages, creating high-quality SVG…

Scaling generative inverse and forward rendering to real-world scenarios is bottlenecked by the limited realism and temporal coherence of existing synthetic datasets. To bridge this persistent domain gap, we introduce a large-scale, dynamic…

The development of high-dimensional generative models has recently gained a great surge of interest with the introduction of variational auto-encoders and generative adversarial neural networks. Different variants have been proposed where…

While generative adversarial networks (GAN) have been widely adopted in various topics, in this paper we generalize the standard GAN to a new perspective by treating realness as a random variable that can be estimated from multiple angles.…

We complete the classification of globally generated vector bundles with small $c_1$ on projective spaces by treating the case $c_1 = 5$ on $\mathbb{P}^n$, $n \geq 4$ (the case $c_1 \leq 3$ has been considered by Sierra and Ugaglia, while…

We investigate the Gopakumar-Vafa (GV) theory of local curves, namely, the total spaces of rank two vector bundles with canonical determinant on smooth projective curves. Under a certain genericity condition on the rank two bundles, we…

Interest in image-to-image translation has grown substantially in recent years with the success of unsupervised models based on the cycle-consistency assumption. The achievements of these models have been limited to a particular subset of…

We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…

Any line bundle $\cl $ on a smooth curve $C$ of genus $g$ with $\deg \cl \ge 2g+1$ is normally generated, i.e., $\varphi_\cl (C)\subseteq \mathbb P H^0 (C,\cl)$ is projectively normal. However, it has known that more various line bundles of…

We present equivalences between certain categories of vector bundles on projective varieties, namely cokernel bundles, Steiner bundles, syzygy bundles, and monads, and full subcategories of representations of certain quivers. As an…

This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also…

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in a previous paper of the authors. The present paper studies bundles which compute these Clifford indices. We show that under…

In this paper we generalise the theory of real vector bundles to a certain class of non-Hausdorff manifolds. In particular, it is shown that every vector bundle fibred over these non-Hausdorff manifolds can be constructed as a colimit of…

What is a good vector representation of an object? We believe that it should be generative in 3D, in the sense that it can produce new 3D objects; as well as be predictable from 2D, in the sense that it can be perceived from 2D images. We…

We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms.…

A new generalization of Grassmannians, called {\nu}-grassmannians, and a canonical super vector bundle over this new space, say {\Gamma}, are introduced. Then, constructing a Gauss supermap of a super vector bundle, the universal property…

Current bundle generation studies focus on generating a combination of items to improve user experience. In real-world applications, there is also a great need to produce bundle creatives that consist of mixture types of objects (e.g.,…

Recent advances in image generation have achieved remarkable visual quality, while a fundamental challenge remains: Can image generation be controlled at the element level, enabling intuitive modifications such as adjusting shapes, altering…

Generative flows are promising tractable models for density modeling that define probabilistic distributions with invertible transformations. However, tractability imposes architectural constraints on generative flows, making them less…