# ⎈ captn's log (PDF)

## 23.8.2021 : Upper bound for the intersection multiplicity

Looks like the bound $z_0 \leq \frac{mD}{t} + m +n$ for might possibly work? Hopefully? ($D=\max\{ \deg(F), \deg(G) \}$).

EDIT 26.8.: it didn't :(

## 13.8.2021 : Upper bound for the intersection multiplicity (PDF)

Since the pyramids were a dissapointment :(

## 11.8.2021 : ssssssssssssssss

## 14.7.2021 : Continuation of the case of difference between and Blow-up (PDF)

This is basically a continuation of the post from **17.5.2021**. The graphs of the branches $C_1$ and $C_2$ mentioned below can be seen here: [LINK TO DESMOS].

## 8.7.2021: A little Corollary (PDF)

This basically says that if the intersection multiplicity is greater than $mn+t$, then it is increased at least by some number of branches. But I think this can be improved a little, it's more like a partial result.

## 18.6.2021: Fixing the mistake from the Project of Disseration (PDF)

## 2.6.2021: I don’t like Omega symbol anymore (i never liked it actually >:-( )

It’s too unspecific. I want to use some kind of spiral. This one will do for now: (ale chcelo by to nejaku usadlejsiu, tato ide moc do vysky). Or maybe something like this could do: (v pripade nudze mozno)? I don’t know.

## 17.05.2021 : Why is the Omega sequence different from the Blow-up (PDF)

Both blowup and our new decomposition (for pair of curves) provide us with a certain sequence of numbers. Sum of this sequence is equal to intersection multiplicity. These sequences are not equal in a sense that two cases having two identical blowup sequences does not imply having identical Omega sequences and vice versa.

Examples of this are below.

Of course, there might be some correlation in certain types of intersections, it just looks like there is none in the general case.

### PLOTS OF THE INTERSECTIONS IN THE EXAMPLES

## june 2021 - i think I'll try to do this again (PDF)

My universal pdf notes are getting confusing.

This post contains most of my pdf notes I have so far, so it's super long. Later posts are planned to be shorter (I hope).