Abstract
We use recent duality results of Eisenbud and Ulrich to give tools to study quadratically enriched residual intersections when there is no excess bundle. We use this to prove a formula for the Witt-valued Euler number of an almost complete intersection. We give example computations of quadratically enriched excess and residual intersections.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS 2001890
Award Identifier / Grant number: DMS 2103838
Funding statement: Kirsten Wickelgren was partially supported by NSF CAREER DMS 2001890 and NSF DMS 2103838.
A Macaulay2 code
We have implemented functions for the computer program Macaulay2 [21] to carry out the computations implicit in Proposition 2.3 for concrete examples, in the case
Below, is a sample session computing a diagonal representative of
We thus find that
Functions Bprime and CDTr from form.m2
Function diagonalize from diagonalization.m2
Acknowledgements
We wish to thank Claudia Polini for introducing us to the paper [15], David Eisenbud for useful discussions (he owes us money as he promised payment for asking questions he can answer), Stephen McKean for useful discussions on [45], and Sabrina Pauli for useful discussions on quadratically enriched excess intersections. Kirsten Wickelgren gratefully thanks Joseph Rabinoff for providing “a room of one’s own” to work on this paper.
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