Matches in SemOpenAlex for { <https://semopenalex.org/work/W2798710129> ?p ?o ?g. }
Showing items 1 to 59 of
59
with 100 items per page.
- W2798710129 abstract "In our previous paper, viewing $D^b(K(l))$ as a non-commutative curve, we observed that it is reasonable to count non-commutative curves in certain triangulated categories, where $K(l)$ is the Kronecker quiver with $l$-arrows. We gave a general definition, which specializes to the non-commutative curve-counting invariants. Roughly it defines the set of subcategories of fixed type in a given category modulo conditions. Here, after recalling the definition, we focus on examples. We compute the non-commutative curve-counting invariants in $D^b(Q)$ for two affine quivers and in $ D^b(A_n)$. We estimate these numbers for $D^b({mathbb P}^2)$, in particular we prove finiteness and that the exact determining of these numbers for $D^b({mathbb P}^2)$ leads to proving (or disproving) of Markov conjecture. Via homological mirror symmetry this gives a new approach to this conjecture. Some of the results proved here were announced in the previous work." @default.
- W2798710129 created "2018-05-07" @default.
- W2798710129 creator A5067549542 @default.
- W2798710129 creator A5085039423 @default.
- W2798710129 date "2018-05-01" @default.
- W2798710129 modified "2023-10-17" @default.
- W2798710129 title "Non-commutative curve-counting invariants" @default.
- W2798710129 hasPublicationYear "2018" @default.
- W2798710129 type Work @default.
- W2798710129 sameAs 2798710129 @default.
- W2798710129 citedByCount "0" @default.
- W2798710129 crossrefType "posted-content" @default.
- W2798710129 hasAuthorship W2798710129A5067549542 @default.
- W2798710129 hasAuthorship W2798710129A5085039423 @default.
- W2798710129 hasConcept C114614502 @default.
- W2798710129 hasConcept C118615104 @default.
- W2798710129 hasConcept C168310172 @default.
- W2798710129 hasConcept C183778304 @default.
- W2798710129 hasConcept C202444582 @default.
- W2798710129 hasConcept C2780990831 @default.
- W2798710129 hasConcept C33923547 @default.
- W2798710129 hasConcept C54732982 @default.
- W2798710129 hasConcept C92757383 @default.
- W2798710129 hasConceptScore W2798710129C114614502 @default.
- W2798710129 hasConceptScore W2798710129C118615104 @default.
- W2798710129 hasConceptScore W2798710129C168310172 @default.
- W2798710129 hasConceptScore W2798710129C183778304 @default.
- W2798710129 hasConceptScore W2798710129C202444582 @default.
- W2798710129 hasConceptScore W2798710129C2780990831 @default.
- W2798710129 hasConceptScore W2798710129C33923547 @default.
- W2798710129 hasConceptScore W2798710129C54732982 @default.
- W2798710129 hasConceptScore W2798710129C92757383 @default.
- W2798710129 hasLocation W27987101291 @default.
- W2798710129 hasOpenAccess W2798710129 @default.
- W2798710129 hasPrimaryLocation W27987101291 @default.
- W2798710129 hasRelatedWork W1520537714 @default.
- W2798710129 hasRelatedWork W1621867678 @default.
- W2798710129 hasRelatedWork W1687415783 @default.
- W2798710129 hasRelatedWork W2750034222 @default.
- W2798710129 hasRelatedWork W2897724939 @default.
- W2798710129 hasRelatedWork W2950919665 @default.
- W2798710129 hasRelatedWork W2951320789 @default.
- W2798710129 hasRelatedWork W2953259898 @default.
- W2798710129 hasRelatedWork W2953347306 @default.
- W2798710129 hasRelatedWork W2963309042 @default.
- W2798710129 hasRelatedWork W2980095922 @default.
- W2798710129 hasRelatedWork W2985205564 @default.
- W2798710129 hasRelatedWork W3037742570 @default.
- W2798710129 hasRelatedWork W3104341195 @default.
- W2798710129 hasRelatedWork W3104356981 @default.
- W2798710129 hasRelatedWork W3106181326 @default.
- W2798710129 hasRelatedWork W3158474099 @default.
- W2798710129 hasRelatedWork W3189284776 @default.
- W2798710129 hasRelatedWork W3213151471 @default.
- W2798710129 hasRelatedWork W80525605 @default.
- W2798710129 isParatext "false" @default.
- W2798710129 isRetracted "false" @default.
- W2798710129 magId "2798710129" @default.
- W2798710129 workType "article" @default.