Let f:X→Y be a semismall resolution of singularities. Then the pushforward of the constant sheaf on X is a semisimple perverse sheaf on Y. Under these conditions, I know how to calculate the direct summands of the pushforward f*ℚX[dim X]. My question is as follows: What more general statements a...
What are situations where one can conclude that all entries of an intersection form are divisible by a fixed integer? More precisely: $F \subset S$ is a proper connected (usually reducible) half-dimensional subvariety of a smooth variety $S$. In this situation one define the "refined intersect...
Let f:X→Y be a semismall resolution of singularities. Then the pushforward of the constant sheaf on X is a semisimple perverse sheaf on Y. Under these conditions, I know how to calculate the direct summands of the pushforward f*ℚX[dim X]. My question is as follows: What more general statements a...
I add a Picture "GaussBonnet with Jpeg format to the following question but it does not work. (Some possible obstructions to ) Limit cycles as closed geodesics(3) Can one help me to resolve this problem?
I am a TA for a multivariable calculus class this semester. I have also TA'd this course a few times in the past. Every time I teach this course, I am never quite sure how I should present curl and divergence. This course follows Stewart's book and does not use differential forms; we only deal wi...
« first day (1753 days earlier) ← previous day next day → last day (2155 days later) »