Fu Haoshuo

Here are some notes that are typed by LaTeX during my study.

Intersection Complex

This note explains the calculation of two examples in the survey paper [dCM09].

The Proof of Decomposition Theorem

This note is used for the seminar in fall 2018, giving the third proof of decomposition theorem by de Cataldo and Migliorini.

"Zeta Function" of Two Special Case

This note gives a straight calculation of the so-called "numerical Perverse=Hodge" result.

Some Corrections in Schnell and Kebekus's Paper

Here is some corrections in the paper by Schnell and Kebekus. These problems does not affect the main results in this paper.

Exceptional Objects of Hilbert Schemes

This note studies the exceptional objects of Hilbert schemes of points on surfaces, especially Fano surfaces.

Here are some notes that are written by hand.

Geometric Satake Equivalence

These 1, 2, 3 are the notes in a seminar in spring 2020, about the proof of geometric Satake equivalence for characteristic zero coefficient field.

The Result of Arkhipov-Bezrukavnikov

These 1, 2, 3, 4 are the notes in a seminar in fall 2020, aiming to prove the equivalence between equivariant sheaves on Springer resolution and Iwahori-Whittaker category.