arXiv subjects
Publications and source records attributed to Jianqiang Yang.
In this paper, we obtain several results on fake quadrics. First, we describe the cones \(\operatorname{Nef}(S)\) and \(\overline{\operatorname{Eff}(S)}\), and then provide a criterion for determining whether a divisor on a fake quadric is ample or effective, respectively. Second, we show that no fake quadric can be embedded into $\mathbb P^4$. Finally, we establish the bounded cohomology property for fake quadrics.
In this article, we find finitely many numerical invariants to classify the diffeomorphism types of three dimensional simply connected Mori fibre spaces with torsion free homology groups.
In this paper, we consider the rationally elliptic projective fourfolds that are holomorphically embedded into the complex projective eight-space $\mathbb{P}^8$. It is proved that a simply-connected $\mathbb Q$-homological projective four-space $X\subset\mathbb{P}^8$ is biholomorphic to $\mathbb P^4$ by using Euler characteristic and Chern numbers formulae of the normal bundle for a holomorphic embedding $i:X \to\mathbb{P}^8$. During the process of proving the result, we incidentally discovered that a $\mathbb{Q}$-homological projective 4-space $X$ with Kodaira dimension $k(X) \neq 4$ is isomorphic to $\mathbb{P}^4$. This finding provides a positive answer to a question posed by Wilson in the case where the dimension $n=4$. Using a similar approach, we show that the Hodge conjecture holds for the rationally elliptic fourfold $X \subset\mathbb{P}^8$, and the rationally elliptic fourfold $X \subset\mathbb{P}^8$ has non-positive Hodge level.
We show some results of compact Kahler manifolds with elliptic homotopy type. In complex dimension 4 we list the Hodge diamonds of compact Kahler manifolds with elliptic homotopy type. In general dimension we obtain a partial characterization of the Hodge diamonds.
Existing summarization systems mostly generate summaries purely relying on the content of the source document. However, even for humans, we usually need some references or exemplars to help us fully understand the source document and write summaries in a particular format. But how to find the high-quality exemplars and incorporate them into summarization systems is still challenging and worth exploring. In this paper, we propose RetrievalSum, a novel retrieval enhanced abstractive summarization framework consisting of a dense Retriever and a Summarizer. At first, several closely related exemplars are retrieved as supplementary input to help the generation model understand the text more comprehensively. Furthermore, retrieved exemplars can also play a role in guiding the model to capture the writing style of a specific corpus. We validate our method on a wide range of summarization datasets across multiple domains and two backbone models: BERT and BART. Results show that our framework obtains significant improvement by 1.38~4.66 in ROUGE-1 score when compared with the powerful pre-trained models, and achieve new state-of-the-art on BillSum. Human evaluation demonstrates that our retrieval enhanced model can better capture the domain-specific writing style.
In this paper we study smooth orientation-preserving free actions of the cyclic group $\mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds, $\sharp g (S^n \times S^n)\sharp Σ$, where $Σ$ is a homotopy $2n$-sphere. When $n=2$ we obtain a classification up to topological conjugation. When $n=3$ we obtain a classification up to smooth conjugation. When $n \ge 4$ we obtain a classification up to smooth conjugation when the prime factors of $m$ are larger than a constant $C(n)$.