Related papers: Virtual global generation in higher dimensions

This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…

We classify nef vector bundles on a projective space with first Chern class three over an algebraically closed field of characteristic zero; we see, in particular, that these nef vector bundles are globally generated if the second Chern…

The subject of the paper is the geometry and topology of cosmological spacetimes and vector bundles thereon, which are used to model physical fields propagating in the universe. Global hyperbolicity and factorization properties of the…

We describe the locus of stable bundles on a smooth genus $g$ curve that fail to be globally generated. For each rank $r$ and degree $d$ with $rg<d<r(2g-1)$, we exhibit a component of the expected dimension. We show moreover that no…

Deep generative models have unlocked another profound realm of human creativity. By capturing and generalizing patterns within data, we have entered the epoch of all-encompassing Artificial Intelligence for General Creativity (AIGC).…

We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally…

Vector graphics are essential in design, providing artists with a versatile medium for creating resolution-independent and highly editable visual content. Recent advancements in vision-language and diffusion models have fueled interest in…

One classifies the globally generated vector bundles on P^3 with the first Chern class c_1=3. The case c_1=2 on P^n was done by J.C. Sierra and L. Ugaglia (see the References) and the case c_1=3, rank=2 on P^n was done by S. Huh (see the…

We propose a novel approach to image generation by decomposing an image into a structured sequence, where each element in the sequence shares the same spatial resolution but differs in the number of unique tokens used, capturing different…

We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes…

We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…

We survey some recent progress in the theory of vector bundles on algebraic varieties and related questions in algebraic K-theory.

In this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle.…

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

Nowadays, there are many diffusion and autoregressive models that show impressive results for generating images from text and other input domains. However, these methods are not intended for ultra-high-resolution image synthesis. Vector…

Deep generative models have shown success in generating 3D shapes with different representations. In this work, we propose Neural Volumetric Mesh Generator(NVMG) which can generate novel and high-quality volumetric meshes. Unlike the…

Recent visual generation models have made major progress in photorealism, typography, instruction following, and interactive editing, yet they still struggle with spatial reasoning, persistent state, long-horizon consistency, and causal…

We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with…