arXiv subjects
Publications and source records attributed to Li Cai.
In this paper we shall illustrate that each polytopal moment-angle complex can be understood as the intersection of the minima of corresponding Siegel leaves and the unit sphere, with respect to the maximum norm. Consequently, an alternative proof of a rigidity theorem of Bosio and Meersseman is obtained; as piecewise linear manifolds, polytopal real moment-angle complexes can be smoothed in a natural way.
A nonzero rational number is called a cube sum if it is of form $a^3+b^3$ with $a,b\in \mathbb{Q}^\times$. In this paper, we prove that for any odd integer $k\geq 1$, there exist infinitely many cube-free odd integers $n$ with exactly $k$ distinct prime factors such that $2n$ is a cube sum (resp. not a cube sum). We give also a general construction of Heegner point and obtain an explicit Gross-Zagier formula which is used to prove the Birch and Swinnerton-Dyer conjecture for certain elliptic curve related to the cube sum problem.
We give an explicit form of Gross-Zagier formula on Shimura Curves and an explicit form of Waldspurger formula.
In this note we prove that the integer cohomology ring of polyhedral products with space pairs $(D^1, S^0)$ can also be described explicitly by a multiplicative Hochster's formula.