论文标题
针对投影歧管的广义蒙格 - 安培方程的数值标准
A numerical criterion for generalised Monge-Ampere equations on projective manifolds
论文作者
论文摘要
我们证明，如果某些交叉点为正数，则广义的monge-ampère方程（包括倒数的黑石方程等方程式，包括$ j $ eqequation等反向的黑石方程，以及蒙格 - ampère方程）。作为我们工作的推论，我们改善了陈（尽管在投影案例中）对$ j $ quequation的解决方案的存在，并证明了SzékelyHidi在预测的情况下对某些反相反方程式的溶解度的猜想。改善陈结果的主要新成分是质量结果的退化浓度。尽管在统一阳性的假设下，我们还证明了我们结果的均等版本。特别是，我们可以在具有大型对称性的歧管上恢复现有结果，例如投射曲折的歧管。
We prove that generalised Monge-Ampère equations (a family of equations which includes the inverse Hessian equations like the $J$-equation, as well as the Monge-Ampère equation) on projective manifolds have smooth solutions if certain intersection numbers are positive. As corollaries of our work, we improve a result of Chen (albeit in the projective case) on the existence of solutions to the $J$-equation, and prove a conjecture of Székelyhidi in the projective case on the solvability of certain inverse Hessian equations. The key new ingredient in improving Chen's result is a degenerate concentration of mass result. We also prove an equivariant version of our results, albeit under the assumption of uniform positivity. In particular, we can recover existing results on manifolds with large symmetry such as projective toric manifolds.
