FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2098396350> ?p ?o ?g. }

• W2098396350 abstract "The aim of this thesis is to investigate certain properties of two constructions of algebraic varieties based on a finite group action. In the first part we investigate Cox rings of minimal resolutions of (complex) surface quotient singularities C/G, where G is a finite (small) subgroup of GL(2,C). As a result we provide two descriptions of these rings. The first one is the single relation between its generators or, in other words, an equation for the spectrum of the Cox ring presented as a hypersurface in an affine space. In addition, we obtain an explicit description of the minimal resolution of C/G as a divisor in a toric variety. The second way of describing the Cox ring of the minimal resolution of C/G ring relies on viewing it as a subring of the coordinate ring of a product of a torus and another surface quotient singularity, C/[G,G]. We give a method of finding a set of generators of such an embedding of the Cox ring, which uses only the information on the intersection numbers of components of the exceptional fibre of the considered resolution and on invariants of the induced action of [G,G] on C. We expect that this idea can be generalized to selected classes of resolutions of quotient singularities in higher dimensions. The second part of the thesis concerns geometric models of Markov processes on phylogenetic trees. We concentrate on the case of phylogenetic trees with symmetries, understood as invariance with respect to a transitive action of a finite group. First we investigate the setting with added assumption of the isotropy of the model. The main result of this part concerns models with groups of symmetries containing large abelian subgroups. We prove that in this case the assumption of isotropy is unnecessary and we use these results to show that hyperbinary models are the only isotropic models with abelian group of symmetries. Then we change the setting: we give up the assumption of isotropy and consider geometric properties of general group-based models and G-models. We give the first examples of non-normal models in these classes and compute Hilbert-Ehrhart polynomials to investigate the deformation equivalence of models for trees with the same number of leaves. Moreover, we propose a (conjectural) method of generating phylogenetic invariants of group-based models and prove that for the 3-Kimura model it is equivalent to an important conjecture of Sturmfels and Sullivant concerning the degree of generation of phylogenetic invariants." @default.
• W2098396350 created "2016-06-24" @default.
• W2098396350 creator A5056912749 @default.
• W2098396350 date "2013-10-08" @default.
• W2098396350 modified "2023-09-27" @default.
• W2098396350 title "Constructing algebraic varieties via finite group actions" @default.
• W2098396350 cites W1555851964 @default.
• W2098396350 cites W1584154100 @default.
• W2098396350 cites W1599833186 @default.
• W2098396350 cites W1701978635 @default.
• W2098396350 cites W1970259072 @default.
• W2098396350 cites W1973505437 @default.
• W2098396350 cites W2002152549 @default.
• W2098396350 cites W2008039602 @default.
• W2098396350 cites W2027430137 @default.
• W2098396350 cites W2040371959 @default.
• W2098396350 cites W2041236400 @default.
• W2098396350 cites W2167242722 @default.
• W2098396350 cites W2324715390 @default.
• W2098396350 cites W2964220995 @default.
• W2098396350 hasPublicationYear "2013" @default.
• W2098396350 type Work @default.
• W2098396350 sameAs 2098396350 @default.
• W2098396350 citedByCount "0" @default.
• W2098396350 crossrefType "dissertation" @default.
• W2098396350 hasAuthorship W2098396350A5056912749 @default.
• W2098396350 hasConcept C114614502 @default.
• W2098396350 hasConcept C118615104 @default.
• W2098396350 hasConcept C134306372 @default.
• W2098396350 hasConcept C165761256 @default.
• W2098396350 hasConcept C178790620 @default.
• W2098396350 hasConcept C185579658 @default.
• W2098396350 hasConcept C185592680 @default.
• W2098396350 hasConcept C199422724 @default.
• W2098396350 hasConcept C202444582 @default.
• W2098396350 hasConcept C2777404646 @default.
• W2098396350 hasConcept C2780378348 @default.
• W2098396350 hasConcept C2781311116 @default.
• W2098396350 hasConcept C33923547 @default.
• W2098396350 hasConcept C92757383 @default.
• W2098396350 hasConcept C9376300 @default.
• W2098396350 hasConceptScore W2098396350C114614502 @default.
• W2098396350 hasConceptScore W2098396350C118615104 @default.
• W2098396350 hasConceptScore W2098396350C134306372 @default.
• W2098396350 hasConceptScore W2098396350C165761256 @default.
• W2098396350 hasConceptScore W2098396350C178790620 @default.
• W2098396350 hasConceptScore W2098396350C185579658 @default.
• W2098396350 hasConceptScore W2098396350C185592680 @default.
• W2098396350 hasConceptScore W2098396350C199422724 @default.
• W2098396350 hasConceptScore W2098396350C202444582 @default.
• W2098396350 hasConceptScore W2098396350C2777404646 @default.
• W2098396350 hasConceptScore W2098396350C2780378348 @default.
• W2098396350 hasConceptScore W2098396350C2781311116 @default.
• W2098396350 hasConceptScore W2098396350C33923547 @default.
• W2098396350 hasConceptScore W2098396350C92757383 @default.
• W2098396350 hasConceptScore W2098396350C9376300 @default.
• W2098396350 hasLocation W20983963501 @default.
• W2098396350 hasOpenAccess W2098396350 @default.
• W2098396350 hasPrimaryLocation W20983963501 @default.
• W2098396350 hasRelatedWork W1531126608 @default.
• W2098396350 hasRelatedWork W1551740593 @default.
• W2098396350 hasRelatedWork W1668567747 @default.
• W2098396350 hasRelatedWork W1836776101 @default.
• W2098396350 hasRelatedWork W1990970604 @default.
• W2098396350 hasRelatedWork W2015587331 @default.
• W2098396350 hasRelatedWork W2022023853 @default.
• W2098396350 hasRelatedWork W2046039590 @default.
• W2098396350 hasRelatedWork W2053467455 @default.
• W2098396350 hasRelatedWork W2169889679 @default.
• W2098396350 hasRelatedWork W2189923182 @default.
• W2098396350 hasRelatedWork W2268721107 @default.
• W2098396350 hasRelatedWork W2949528075 @default.
• W2098396350 hasRelatedWork W2962723190 @default.
• W2098396350 hasRelatedWork W2963440250 @default.
• W2098396350 hasRelatedWork W2963493085 @default.
• W2098396350 hasRelatedWork W3043744776 @default.
• W2098396350 hasRelatedWork W3082401770 @default.
• W2098396350 hasRelatedWork W3091771995 @default.
• W2098396350 hasRelatedWork W560534796 @default.
• W2098396350 isParatext "false" @default.
• W2098396350 isRetracted "false" @default.
• W2098396350 magId "2098396350" @default.
• W2098396350 workType "dissertation" @default.