Matches in SemOpenAlex for { <https://semopenalex.org/work/W4310290426> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W4310290426 abstract "Consider a field $k$ of characteristic $0$, not necessarily algebraically closed, and a fixed algebraic curve $f=0$ defined by a tame polynomial $fin k[x,y]$ with only quasi-homogeneous singularities. We prove that the space of holomorphic foliations in the plane ${mathbb A}^2_k$ having $f=0$ as a fixed invariant curve is generated as $k[x,y]$-module by at most four elements, three of them are the trivial foliations $fdx,fdy$ and $df$. Our proof is algorithmic and constructs the fourth foliation explicitly. Using Serre's GAGA and Quillen-Suslin theorem, we show that for a suitable field extension $K$ of $k$ such a module over $K[x,y]$ is actually generated by two elements, and therefore, such curves are free divisors in the sense of K. Saito. After performing Groebner basis for this module, we observe that in many well-known examples, $K=k$." @default.
- W4310290426 created "2022-11-30" @default.
- W4310290426 creator A5056554162 @default.
- W4310290426 creator A5062049297 @default.
- W4310290426 date "2021-01-21" @default.
- W4310290426 modified "2023-09-26" @default.
- W4310290426 title "Algebraic curves and foliations" @default.
- W4310290426 doi "https://doi.org/10.48550/arxiv.2101.08627" @default.
- W4310290426 hasPublicationYear "2021" @default.
- W4310290426 type Work @default.
- W4310290426 citedByCount "0" @default.
- W4310290426 crossrefType "posted-content" @default.
- W4310290426 hasAuthorship W4310290426A5056554162 @default.
- W4310290426 hasAuthorship W4310290426A5062049297 @default.
- W4310290426 hasBestOaLocation W43102904261 @default.
- W4310290426 hasConcept C127313418 @default.
- W4310290426 hasConcept C12843 @default.
- W4310290426 hasConcept C134306372 @default.
- W4310290426 hasConcept C168425004 @default.
- W4310290426 hasConcept C17409809 @default.
- W4310290426 hasConcept C190470478 @default.
- W4310290426 hasConcept C202444582 @default.
- W4310290426 hasConcept C203701370 @default.
- W4310290426 hasConcept C204575570 @default.
- W4310290426 hasConcept C207043602 @default.
- W4310290426 hasConcept C26687426 @default.
- W4310290426 hasConcept C33923547 @default.
- W4310290426 hasConcept C37914503 @default.
- W4310290426 hasConcept C43809302 @default.
- W4310290426 hasConcept C68363185 @default.
- W4310290426 hasConcept C90119067 @default.
- W4310290426 hasConcept C9376300 @default.
- W4310290426 hasConcept C9652623 @default.
- W4310290426 hasConceptScore W4310290426C127313418 @default.
- W4310290426 hasConceptScore W4310290426C12843 @default.
- W4310290426 hasConceptScore W4310290426C134306372 @default.
- W4310290426 hasConceptScore W4310290426C168425004 @default.
- W4310290426 hasConceptScore W4310290426C17409809 @default.
- W4310290426 hasConceptScore W4310290426C190470478 @default.
- W4310290426 hasConceptScore W4310290426C202444582 @default.
- W4310290426 hasConceptScore W4310290426C203701370 @default.
- W4310290426 hasConceptScore W4310290426C204575570 @default.
- W4310290426 hasConceptScore W4310290426C207043602 @default.
- W4310290426 hasConceptScore W4310290426C26687426 @default.
- W4310290426 hasConceptScore W4310290426C33923547 @default.
- W4310290426 hasConceptScore W4310290426C37914503 @default.
- W4310290426 hasConceptScore W4310290426C43809302 @default.
- W4310290426 hasConceptScore W4310290426C68363185 @default.
- W4310290426 hasConceptScore W4310290426C90119067 @default.
- W4310290426 hasConceptScore W4310290426C9376300 @default.
- W4310290426 hasConceptScore W4310290426C9652623 @default.
- W4310290426 hasLocation W43102904261 @default.
- W4310290426 hasOpenAccess W4310290426 @default.
- W4310290426 hasPrimaryLocation W43102904261 @default.
- W4310290426 hasRelatedWork W1967668701 @default.
- W4310290426 hasRelatedWork W1977919980 @default.
- W4310290426 hasRelatedWork W2028713195 @default.
- W4310290426 hasRelatedWork W2047467954 @default.
- W4310290426 hasRelatedWork W2049292717 @default.
- W4310290426 hasRelatedWork W2142177650 @default.
- W4310290426 hasRelatedWork W2739524669 @default.
- W4310290426 hasRelatedWork W2912507129 @default.
- W4310290426 hasRelatedWork W4297953879 @default.
- W4310290426 hasRelatedWork W4379983011 @default.
- W4310290426 isParatext "false" @default.
- W4310290426 isRetracted "false" @default.
- W4310290426 workType "article" @default.