conormal module

[Hans-Christian Herbig]

Hello,

I have a rather basic question.

How can I compute the syzygies of I/I^2 in the following example?

R=QQ[q1,q2,p1,p2]
I=ideal(q1*p2,q2*p1,q1*p1-q2*p2)

I am struggeling with the syntax.

Thank you, Hans-Christian Herbig.

[Jürgen Böhm]

I assume you would like to compute the free resolution of I/I^2 as an R/I module.

Not being absolutely sure, that this is the right way to do it, but for me

S = R/I

J = I/I^2 ** S

resol = res J

looks promising.

Jürgen

[Jürgen Böhm]

Sorry, it must be

J = (I/I^2) ** S

(The parentheses are important).

Greetings,

Jürgen

herb...@gmail.com schrieb am Dienstag, 4. Februar 2025 um 03:25:12 UTC+1:

[Hans-Christian Herbig]

Dear Jürgen,

R=QQ[q1,q2,p1,p2]

I=ideal(q1*p2,q2*p1,q1*p1-q2*p2) 

Q=R/I

M=(I/I^2)**Q

gives

cokernel {2}000000p12000−q22{2}000000−p22000q12{2}000000−p1p2000−q1q2​​{2}0{2}0{2}0​000​000​000​000​000​p12−p22−p1p2​000​000​000​−q22q12−q1q2​​

which is not plausible because the ideal is bigraded of degree (1,1)

and the answer is not.

HC