Study note · exact algebra calculation
Read the recordFive points, two tangent spaces
An exact comparison of two Artinian quotients with Hilbert function (1, 3, 1).
Study notes
Classical results understood through proofs, worked examples, and exact calculations. These notes record learning and review.
Study note · chain calculation
Read the recordWhere characteristic enters a resolution
From a six-vertex projective plane to two different Betti numbers.
Study note · classical criterion
Read the recordTwo negative Pell equations that coarse data cannot separate
145 and 305: matching congruence signatures, opposite integral answers.
Study note · worked proof
Read the recordThe relations of (ab, bc, ca)
My question about “rank-two freeness” leads to a relation module, an exact resolution, and three ways to check it.
A worked example
Two length-five algebras share a Hilbert function. The notes distinguish their multiplication, full embedded tangent spaces, and graded restrictions.
From the study notes
Same Hilbert function.
Different deformations.
21
dim HomS(I, S/I)
Classical example · assistant-prepared calculationRead the study note