Timeline for Questions about the article "A tour of the strong and weak Lefschetz properties"
Current License: CC BY-SA 4.0
5 events
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| Mar 3, 2023 at 16:13 | comment | added | Sam Hopkins | In fact on pg. 6 (not pg. 10) of the pdf you linked to, it says exactly that: "If $A$ is a Gorenstein ring of dimension $d$, then $A$ is said to have the WLP if a general artinian reduction of $A$ has the WLP, that is, if $A/\langle L_1, \ldots, L_d \rangle$ has the WLP, where $L_1,\ldots,L_d \in A$ are general forms of degree 1." | |
| Mar 3, 2023 at 14:17 | comment | added | Sam Hopkins | General artinian reduction usually means you quotient by the appropriate number of generic linear forms to produce an artinian algebra. | |
| Mar 3, 2023 at 1:48 | comment | added | Donu Arapura | "General" in algebraic geometry, and related areas, means that the construction or statement is valid for an open dense set of the parameter space. Often it is left up to you to decide what the parameter space is, e.g. in the case of complete intersection it might be the space of $n$-tuples of defining polynomials. Perhaps you can ask the authors for more specific questions about their paper. | |
| S Mar 3, 2023 at 0:37 | review | First questions | |||
| Mar 3, 2023 at 1:05 | |||||
| S Mar 3, 2023 at 0:37 | history | asked | syzybees | CC BY-SA 4.0 |