examples of toric varieties

Last modified date: <%+ tp.file.last_modified_date() %>



examples of toric varieties

Zero: Gnm

attachments/Pasted%20image%2020220625180536.png

A full basis: An

attachments/Pasted%20image%2020220625180623.png

P1

attachments/Pasted%20image%2020220625180722.png

attachments/Pasted%20image%2020220620174930.png

P2

attachments/Pasted%20image%2020220625182116.png attachments/Pasted%20image%2020220625182132.png

Pn

attachments/Pasted%20image%2020220620160256.png attachments/Pasted%20image%2020220620174012.png attachments/Pasted%20image%2020220620174042.png attachments/Pasted%20image%2020220620154615.png

P1×P1

attachments/Pasted%20image%2020220620151809.png

attachments/Pasted%20image%2020220620152526.png

Weighted projective spaces

P(1,1,2)

attachments/Pasted%20image%2020220620173926.png

Cuspidal curves

The cuspidal curve V(x3y2){(t2,t3)|tC2A2 is an affine toric variety: C={(t2,t3)|t0}V(x3y2)

Rational normal curves Cd

attachments/Pasted%20image%2020220620152423.png

Rational normal scrolls

attachments/Pasted%20image%2020220620174119.png

The Hirzebruch surface Hr

attachments/Pasted%20image%2020220625182506.png attachments/Pasted%20image%2020220625182517.png

Dual cones and faces

attachments/Pasted%20image%2020220620180817.png

Cone over a quadric

attachments/Pasted%20image%2020220625180654.png attachments/Pasted%20image%2020220625184149.png

Cone over the rational normal curve

attachments/Pasted%20image%2020220625194901.png

Misc

attachments/Pasted%20image%2020220621115247.png

SpecC[x,y,z]/x2yz

attachments/Pasted%20image%2020220621235637.png This yields a union of cones: attachments/Pasted%20image%2020220621235819.png

Blowups

attachments/Pasted%20image%2020220625181946.png attachments/Pasted%20image%2020220622002411.png

Examples of cones and fans

attachments/Pasted%20image%2020220621214743.png attachments/Pasted%20image%2020220621214845.png

attachments/Pasted%20image%2020220621213111.png

Exercises

attachments/Pasted%20image%2020220625182618.png

attachments/Pasted%20image%2020220806151249.png

Links to this page
#research/dynkin-project #AG/toric #todo/add-references #todo/create-links