--- date: 2022-09-14 13:51 modification date: Wednesday 14th September 2022 13:51:02 title: "2022-09-14" aliases: [2022-09-14] --- Last modified date: <%+ tp.file.last_modified_date() %> --- - Tags: - #AG/toric - Refs: - #todo/add-references - Links: - #todo/create-links --- # 2022-09-14 ![](attachments/Pasted%20image%2020220914135106.png) ![](attachments/Pasted%20image%2020220914140212.png) ![](attachments/Pasted%20image%2020220914140220.png) ![](attachments/Pasted%20image%2020220914141022.png) ![](attachments/Pasted%20image%2020220914141030.png) ![](attachments/Pasted%20image%2020220914141049.png) ![](attachments/Pasted%20image%2020220914141446.png) ![](attachments/Pasted%20image%2020220914141502.png) ![](attachments/Pasted%20image%2020220914144437.png) ![](attachments/Pasted%20image%2020220914144506.png) ![](attachments/Pasted%20image%2020220914144537.png) ![](attachments/Pasted%20image%2020220914144625.png) ![](attachments/Pasted%20image%2020220914144820.png) ![](attachments/Pasted%20image%2020220914144849.png) ![](attachments/Pasted%20image%2020220914145144.png) ![](attachments/Pasted%20image%2020220914144833.png) ![](attachments/Pasted%20image%2020220914150915.png) ![](attachments/Pasted%20image%2020220914152625.png) ![](attachments/Pasted%20image%2020220914152808.png) ![](attachments/Pasted%20image%2020220914153724.png) ![](attachments/Pasted%20image%2020220914153922.png) ![](attachments/Pasted%20image%2020220914154140.png) ![](attachments/Pasted%20image%2020220914154445.png) ![](attachments/Pasted%20image%2020220914154551.png) See [[star subdivision]]. ![](attachments/Pasted%20image%2020220914160656.png) # Divisor theory for toric varieties ![](attachments/Pasted%20image%2020220914184622.png) ![](attachments/Pasted%20image%2020220914184632.png) ![](attachments/Pasted%20image%2020220914184651.png) ![](attachments/Pasted%20image%2020220914185803.png) ![](attachments/Pasted%20image%2020220914190600.png) ![](attachments/Pasted%20image%2020220914191242.png) ![](attachments/Pasted%20image%2020220914191304.png) ![](attachments/Pasted%20image%2020220914191315.png) ![](attachments/Pasted%20image%2020220914191454.png) ![](attachments/Pasted%20image%2020220914191854.png) ![](attachments/Pasted%20image%2020220914191913.png) Summary: if $D = \sum_\rho a_\rho D_\rho$ is Cartier, then there exist $m_\sigma\in M$ for each $\sigma \in \Sigma$ such that $D = \sum_\rho - \ip{m_\sigma}{u_\rho} D_\rho$. ![](attachments/Pasted%20image%2020220914192648.png) ![](attachments/Pasted%20image%2020220914192856.png) ![](attachments/Pasted%20image%2020220914192928.png) ![](attachments/Pasted%20image%2020220914192832.png) ![](attachments/Pasted%20image%2020220914193226.png) ![](attachments/Pasted%20image%2020220914193404.png) ![](attachments/Pasted%20image%2020220914193739.png) ![](attachments/Pasted%20image%2020220914201446.png)