2022-09-10

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2022-09-10

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When Weil are Cartier attachments/Pasted%20image%2020220910221638.png attachments/Pasted%20image%2020220910221649.png

Cartier data: attachments/Pasted%20image%2020220910221927.png

Theorems: attachments/Pasted%20image%2020220910222053.png

attachments/Pasted%20image%2020220912132252.png attachments/Pasted%20image%2020220912133131.png attachments/Pasted%20image%2020220912133645.png attachments/Pasted%20image%2020220912133827.png attachments/Pasted%20image%2020220912133946.png attachments/Pasted%20image%2020220912135600.png attachments/Pasted%20image%2020220912135656.png attachments/Pasted%20image%2020220912135738.png

\begin{align*} \left(D_{\Delta}\right)^n=n ! \operatorname{vol}(\Delta) \end{align*} attachments/Pasted%20image%2020220912140158.png attachments/Pasted%20image%2020220912140248.png attachments/Pasted%20image%2020220912140326.png

attachments/Pasted%20image%2020220912140337.png attachments/Pasted%20image%2020220913144520.png attachments/Pasted%20image%2020220913151810.png attachments/Pasted%20image%2020220913151930.png attachments/Pasted%20image%2020220913155158.png attachments/Pasted%20image%2020220913155227.png

See cone multiplicity.

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See Riemann-Roch.

attachments/Pasted%20image%2020220913162606.png attachments/Pasted%20image%2020220913162652.png attachments/Pasted%20image%2020220913162718.png attachments/Pasted%20image%2020220913164109.png

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Example: cohomology for a 3-dimensional toric variety attachments/Pasted%20image%2020220913165135.png attachments/Pasted%20image%2020220913165143.png

See log forms.

Denominator in definition of Chow, i.e. what is rational equivalence?

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Intersecting a Cartier divisor with a subvariety: attachments/Pasted%20image%2020220913171611.png

Doing this torically: attachments/Pasted%20image%2020220913171809.png attachments/Pasted%20image%2020220913171845.png attachments/Pasted%20image%2020220913171909.png

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Betti numbers: attachments/Pasted%20image%2020220913172657.png

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Links to this page
#unsorted #AG/toric #todo/add-references #todo/create-links