Related papers: A question on klt type varieties of Han and Jiang

In this paper, we define the notion of asymptotically flat divisor on a normal variety over $\C$, and prove that if $X$ is a strongly $F$-regular type variety and $K_X$ is asymptotically flat, then $X$ is of klt type.

We answer a question of Koll\'ar and Kov\'acs by constructing a flat projective morphism to a smooth curve whose fibers are Cohen--Macaulay and reduced, whose generic fiber is smooth, and for which the first cohomology of the structure…

We show that the total Cartier index of varieties with rational singularities in a bounded family is bounded. This solves a problem of Han and Jiang. The overall structure of the proof, which treats the surface case and the…

We introduce the notion of potentially klt pairs for normal projective varieties with pseudoeffective anticanonical divisor. The potentially non-klt locus is a subset of $X$ which is birationally transformed precisely into the non-klt locus…

We present the construction of a large class of homogeneous KT, HKT and QKT manifolds, $G/K$, using an invariant metric on $G$ and the canonical connection. For this a decomposition of the Lie algebra of $G$ is employed, which is most…

We prove the existence of a Quillen Flat Model Structure in the category of unbounded complexes of h-unitary modules over a nonunital ring (or a $k$-algebra, with $k$ a field). This model structure provides a natural framework where a…

Conversational AI and Question-Answering systems (QASs) for knowledge graphs (KGs) are both emerging research areas: they empower users with natural language interfaces for extracting information easily and effectively. Conversational AI…

For any flat projective family $(\mX,\mL)\rightarrow C$ such that the generic fibre $\mX_\eta$ is a klt Q-Fano variety and $\mL|_{\mX_\eta}\sim_{Q}-K_{X_{\eta}}$, we use the techniques from the minimal model program (MMP) to modify the…

In the context of uniformisation problems, we study projective varieties with klt singularities whose cotangent sheaf admits a projectively flat structure over the smooth locus. Generalising work of Jahnke-Radloff, we show that torus…

We complete the classification of compact Hermitian manifolds admitting a flat Gauduchon connection. In particular, we establish a conjecture of Yang and Zheng, showing that apart from the cases of a flat Chern or Bismut connection, such…

We introduce Open Horn Type Theory (OHTT), an extension of dependent type theory with two primitive judgment forms: coherence and gap, subject to a mutual exclusion law. Unlike classical or intuitionistic negation, gap is not defined via…

Generative AI models continue to become more powerful. The launch of ChatGPT in November 2022 has ushered in a new era of AI. ChatGPT and other similar chatbots have a range of capabilities, from answering student homework questions to…

In this article, we show that a flat morphism of $k$-varieties ($\mathop{\mathrm{char}} k=0$) with locally constant geometric fibers becomes finite \'etale after reduction. When $k$ is a real closed field, we prove that such a morphism…

ChatGPT is a language model based on Generative AI. Existing research work on ChatGPT focused on its use in various domains. However, its potential for Sign Language Translation (SLT) is yet to be explored. This paper addresses this void.…

Let \Gamma be a finite group and (V,q) be a regular quadratic \Gamma-form defined over an integral domain $\mathcal{O}_S$ of a global function field (of odd characteristic). We use flat cohomology to classify the quadratic \Gamma-forms…

Conversational Question Answering over Knowledge Graphs (KGs) combines the factual grounding of KG-based QA with the interactive nature of dialogue systems. KGs are widely used in enterprise and domain applications to provide structured,…

We show that the factorial and Q-factorial loci of algebraic varieties defined over an algebraically closed field are open, that products of locally factorial varieties are still locally factorial, and that this property remains true for…

ChatGPT is a powerful large language model (LLM) that covers knowledge resources such as Wikipedia and supports natural language question answering using its own knowledge. Therefore, there is growing interest in exploring whether ChatGPT…

Kleene algebras with tests (KATs) offer sound, complete, and decidable equational reasoning about regularly structured programs. Interest in KATs has increased greatly since NetKAT demonstrated how well extensions of KATs with…

The rapid adoption of generative language models has brought about substantial advancements in digital communication, while simultaneously raising concerns regarding the potential misuse of AI-generated content. Although numerous detection…