For colinked chains, the associated linked projective space is a reduced local complete intersection with rational equidimensional components, diagonal Hilbert polynomial, and the scheme satisfies a Riemann inequality on two-component curves.
Limit linear series: combinatorial theory
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We develop a purely combinatorial theory of limit linear series on metric graphs. This will be based on the formalisms of hypercube rank functions and slope structures. We provide a full classification of combinatorial limit linear series of rank one, and discuss connections to other concepts in tropical algebra and combinatorial algebraic geometry.
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Degenerations of maps to projective spaces
For colinked chains, the associated linked projective space is a reduced local complete intersection with rational equidimensional components, diagonal Hilbert polynomial, and the scheme satisfies a Riemann inequality on two-component curves.