Matches in SemOpenAlex for { <https://semopenalex.org/work/W4289598173> ?p ?o ?g. }
Showing items 1 to 50 of
50
with 100 items per page.
- W4289598173 abstract "Given an irreducible projective variety $X$, the covering gonality of $X$ is the least gonality of an irreducible curve $Esubset X$ passing through a general point of $X$. In this paper we study the covering gonality of the $k$-fold symmetric product $C^{(k)}$ of a smooth complex projective curve $C$ of genus $ggeq k+1$. It follows from a previous work of the first author that the covering gonality of the second symmetric product of $C$ equals the gonality of $C$. Using a similar approach, we prove the same for the $3$-fold and the $4$-fold symmetric product of $C$. Furthermore, we prove that if $2leq kleq 4$ and $C$ is a general curve of genus $ggeq k+4$, the only curves computing the covering gonality of $C^{(k)}$ are copies of $C$ of the form $C+p$, for some point $pin C^{(k-1)}$. A crucial point in the proof is the study of Cayley-Bacharach condition on Grassmannians. In particular, we describe the geometry of linear subspaces of $mathbb{P}^n$ satisfying this condition and we prove a result bounding the dimension of their linear span." @default.
- W4289598173 created "2022-08-03" @default.
- W4289598173 creator A5060147242 @default.
- W4289598173 creator A5067005173 @default.
- W4289598173 date "2022-08-01" @default.
- W4289598173 modified "2023-10-16" @default.
- W4289598173 title "Covering gonality of symmetric products of curves and Cayley-Bacharach condition on Grassmannians" @default.
- W4289598173 doi "https://doi.org/10.48550/arxiv.2208.00990" @default.
- W4289598173 hasPublicationYear "2022" @default.
- W4289598173 type Work @default.
- W4289598173 citedByCount "0" @default.
- W4289598173 crossrefType "posted-content" @default.
- W4289598173 hasAuthorship W4289598173A5060147242 @default.
- W4289598173 hasAuthorship W4289598173A5067005173 @default.
- W4289598173 hasBestOaLocation W42895981731 @default.
- W4289598173 hasConcept C114614502 @default.
- W4289598173 hasConcept C12362212 @default.
- W4289598173 hasConcept C157369684 @default.
- W4289598173 hasConcept C2524010 @default.
- W4289598173 hasConcept C33676613 @default.
- W4289598173 hasConcept C33923547 @default.
- W4289598173 hasConcept C59822182 @default.
- W4289598173 hasConcept C86803240 @default.
- W4289598173 hasConcept C90673727 @default.
- W4289598173 hasConceptScore W4289598173C114614502 @default.
- W4289598173 hasConceptScore W4289598173C12362212 @default.
- W4289598173 hasConceptScore W4289598173C157369684 @default.
- W4289598173 hasConceptScore W4289598173C2524010 @default.
- W4289598173 hasConceptScore W4289598173C33676613 @default.
- W4289598173 hasConceptScore W4289598173C33923547 @default.
- W4289598173 hasConceptScore W4289598173C59822182 @default.
- W4289598173 hasConceptScore W4289598173C86803240 @default.
- W4289598173 hasConceptScore W4289598173C90673727 @default.
- W4289598173 hasLocation W42895981731 @default.
- W4289598173 hasLocation W42895981732 @default.
- W4289598173 hasOpenAccess W4289598173 @default.
- W4289598173 hasPrimaryLocation W42895981731 @default.
- W4289598173 hasRelatedWork W1607154928 @default.
- W4289598173 hasRelatedWork W1967227547 @default.
- W4289598173 hasRelatedWork W1969219531 @default.
- W4289598173 hasRelatedWork W1978042415 @default.
- W4289598173 hasRelatedWork W1990725943 @default.
- W4289598173 hasRelatedWork W2014003871 @default.
- W4289598173 hasRelatedWork W2019425011 @default.
- W4289598173 hasRelatedWork W3096437586 @default.
- W4289598173 hasRelatedWork W4211126889 @default.
- W4289598173 hasRelatedWork W4254355384 @default.
- W4289598173 isParatext "false" @default.
- W4289598173 isRetracted "false" @default.
- W4289598173 workType "article" @default.