---
date: 2022-11-06 00:28
modification date: Sunday 6th November 2022 00:28:54
title: "2022-11-06 Griffiths Harris Surface Notes"
aliases: [2022-11-06]
---

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---

- Tags: 
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- Refs:
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---

# 2022-11-06 Griffiths Harris Surface Notes

![](attachments/Pasted%20image%2020221106010043.png)

![](attachments/Pasted%20image%2020221106002932.png)
![](attachments/Pasted%20image%2020221106003020.png)
![](attachments/Pasted%20image%2020221106003133.png)

![](attachments/Pasted%20image%2020221106003235.png)
![](attachments/Pasted%20image%2020221106003251.png)
![](attachments/Pasted%20image%2020221106003333.png)
![](attachments/Pasted%20image%2020221106003439.png)
![](attachments/Pasted%20image%2020221106003701.png)
Proof: find a bundle $L\to M$ which is positive enough to have global sections away from $C$, but trivial over $C$.

![](attachments/Pasted%20image%2020221106003908.png)
![](attachments/Pasted%20image%2020221106004041.png)
![](attachments/Pasted%20image%2020221106004105.png)

Using theorems:
![](attachments/Pasted%20image%2020221106004258.png)

![](attachments/Pasted%20image%2020221106005230.png)
![](attachments/Pasted%20image%2020221106005316.png)
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![](attachments/Pasted%20image%2020221106010009.png)
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![](attachments/Pasted%20image%2020221106010246.png)
![](attachments/Pasted%20image%2020221106010326.png)
![](attachments/Pasted%20image%2020221106010419.png)

![](attachments/Pasted%20image%2020221106010444.png)
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![](attachments/Pasted%20image%2020221106010758.png)
![](attachments/Pasted%20image%2020221106011034.png)
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![](attachments/Pasted%20image%2020221106011203.png)
![](attachments/Pasted%20image%2020221106011350.png)
![](attachments/Pasted%20image%2020221106011442.png)

![](attachments/Pasted%20image%2020221106011645.png)
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![](attachments/Pasted%20image%2020221106012805.png)
![](attachments/Pasted%20image%2020221106012824.png)
![](attachments/Pasted%20image%2020221106012845.png)
![](attachments/Pasted%20image%2020221106012937.png)

![](attachments/Pasted%20image%2020221106013001.png)
![](attachments/Pasted%20image%2020221106013117.png)
![](attachments/Pasted%20image%2020221106013131.png)

![](attachments/Pasted%20image%2020221106013147.png)
![](attachments/Pasted%20image%2020221106013158.png)

![](attachments/Pasted%20image%2020221106013222.png)

![](attachments/Pasted%20image%2020221106013255.png)

![](attachments/Pasted%20image%2020221106013328.png)
![](attachments/Pasted%20image%2020221106013354.png)

![](attachments/Pasted%20image%2020221106013545.png)
![](attachments/Pasted%20image%2020221106013608.png)

![](attachments/Pasted%20image%2020221106013830.png)
![](attachments/Pasted%20image%2020221106014144.png)