4 papers
Nef cone and successive minima: an example
Ruoyi Guo, Xinyi Yuan
In this paper, we compute the nef cone and the pseudo-effective cone of for a smooth projective curve and its Jacobian variety such that has the min…
Quantitativity on the number of rational points in the Mordell conjecture
Jiawei Yu, Xinyi Yuan, Shengxuan Zhou
In this paper, we prove an explicit upper bound on the number of rational points on a smooth projective curve of genus at least two over a number field. This gives explicit constan…
On Vojta's proof of the Mordell conjecture
Xinyi Yuan
This paper re-organizes Vojta's proof of the Mordell conjecture (i.e. Faltings' theorem) in terms of Arakelov geometry. A new ingredient is to replace an application of Gillet--Sou…
IKSel: Selecting Good Seed Joint Values for Fast Numerical Inverse Kinematics Iterations
Xinyi Yuan, Weiwei Wan, Kensuke Harada
This paper revisits the numerical inverse kinematics (IK) problem, leveraging modern computational resources and refining the seed selection process to develop a solver that is com…