WebJan 8, 2024 · Then the covering gonality of S is { {\mathrm {cov.gon}}} (S)=d-2, and any family of irreducible curves computing the covering gonality is equivalent to (a subfamily of) one of the families described in Example 3.4 of the original paper. Example Assume that there exist two rational curves R_1,R_2\subset S. WebDec 15, 2024 · The gonality of an algebraic curve defined over a number field is bounded from below by the stable gonality of the intersection dual graph of its reduction modulo any prime ideal of the number field. This makes stable gonality of graphs relevant for number theoretic problems (e.g. [17]).
Computing graph gonality is hard - ScienceDirect
WebJan 8, 2024 · Then the covering gonality of S is \({{\mathrm{cov.gon}}}(S)=d-2,\) and any family of irreducible curves computing the covering gonality is equivalent to (a subfamily of) one of the families described in Example 3.4 of the original paper. Example. Assume that there exist two rational curves \(R_1,R_2\subset S\). WebAbstract This thesis is divided into three parts. In the first, we define the covering gonality and separable covering gonality of varieties over fields of positive characteristic, … pit bull rescue washington
Covering gonalities in positive characteristic Mathematics
Webthat covering gonality four is in fact achieved by an (essentially) unique explicit family of curves and the same for connecting gonality five, which we now describe. Given a line ℓ ⊂ X, one defines the incidence divisor Dℓ ⊂ S parametrising lines is either of first or of second type. The locus of lines of second type for a general WebMay 1, 2024 · Since cov. gon (Y) = 1 is equivalent to Y being uniruled, we can think of the covering gonality as a measure of the failure of Y to be uniruled. The following theorem is probably the most general result governing the gonality of moving curves in a very general hypersurface of large degree. WebThe gonality (also called divisorial gonality) gon(G) of a (finite) graph G is the minimum degree of a rank 1 divisor on that graph. It can be thought of as the minimum number of chips that can be placed on that graph such that a debt of 1 can be eliminated via "chip-firing moves" over all possible debt placements. stick fabric to wood