Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  exhibit sharp upper bounds for the probability distribution of the distance from a system of multivariate polynomial equations to the strata of all systems having a critical zero of given corank.  also prove sharp upper bounds for the probability distribution of the condition number of singular systems of multivariate polynomial equations.  finally state a new and sharp technique of the Geometry of Numbers. Using this technique  show that rational systems of multivariate polynomial equations are equidistributed with respect to singular systems having a critical zero of given corank.
['Carlos Beltrán', 'Luis Miguel Pardo']
I am writing a research paper on a idea On the probability distribution of singular varieties of given corank
[{"from": "human", "value": "I am writing a research paper on a idea On the probability distribution of singular varieties of given corank"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  exhibit sharp upper bounds for the probability distribution of the distance from a system of multivariate polynomial equations to the strata of all systems having a critical zero of given corank.  also prove sharp upper bounds for the probability distribution of the condition number of singular systems of multivariate polynomial equations.  finally state a new and sharp technique of the Geometry of Numbers. Using this technique  show that rational systems of multivariate polynomial equations are equidistributed with respect to singular systems having a critical zero of given corank."}]