Computing A1-Euler numbers with Macaulay2
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910770590121984 |
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| author | Pauli, Sabrina |
| author_facet | Pauli, Sabrina |
| contents | We use Macaulay2 for several enriched counts in GW(k). First, we compute the count of lines on a general cubic surface using Macaulay2 over Fp in GW(Fp) for p a prime number and over the rational numbers Q in GW(Q). This gives a new proof for the fact that the count of lines on a cubic surface is 3+12h in GW(k) where h denotes the hyperbolic form. Then, we compute the count of lines in P3 meeting 4 general lines, the count of lines on a quadratic surface meeting one general line and the count of singular elements in a pencil of degree d-surfaces. Finally, we provide code to compute the EKL-form and compute several A1-Milnor numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_01775 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Computing A1-Euler numbers with Macaulay2 Pauli, Sabrina Algebraic Geometry 14N15, 14G27(Primary) 14F42, 14-04 (Secondary) We use Macaulay2 for several enriched counts in GW(k). First, we compute the count of lines on a general cubic surface using Macaulay2 over Fp in GW(Fp) for p a prime number and over the rational numbers Q in GW(Q). This gives a new proof for the fact that the count of lines on a cubic surface is 3+12h in GW(k) where h denotes the hyperbolic form. Then, we compute the count of lines in P3 meeting 4 general lines, the count of lines on a quadratic surface meeting one general line and the count of singular elements in a pencil of degree d-surfaces. Finally, we provide code to compute the EKL-form and compute several A1-Milnor numbers. |
| title | Computing A1-Euler numbers with Macaulay2 |
| topic | Algebraic Geometry 14N15, 14G27(Primary) 14F42, 14-04 (Secondary) |
| url | https://arxiv.org/abs/2003.01775 |