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Degenerate toric varieties

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Kumar Sannidhya Shukla

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Sep 3, 2024, 6:20:35 PM9/3/24
to Macaulay2
Hello,

Suppose X is the 2-dimensional toric variety given by the fan consisting of a single ray, span(1, 0).

rayList = {{1, 0}}
coneList = {{0}}
X = normalToricVariety (rayList, coneList)

I am trying to create the Stanley-Reisner ring for X. Creating it from its fan using the stanleyReisnerRing method gives :

i4 : stanleyReisnerRing (fan (X))
../../build/M2/share/Macaulay2/Core/quotring.m2:153:27:(1):[2]: err
or: expected ideal of the same ring

whereas creating it using dual of the monomial ideal gives,

i5 : (ring X)/(dual monomialIdeal X)
../../build/M2/share/Macaulay2/NormalToricVarieties/Sheaves.m2:8:13
:(2):[2]: -- not yet implemented for degenerate varieties

In this case I am expecting to get just a polynomial ring in 1 variable but I would like to compute more complex examples. Here I just gave the simplest one where it fails.
Is it happening because its degenerate? Is there a way around this?

Best regards,
Kumar.



Best regards,
Kumar
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