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A limit linear series moduli scheme
We develop a new, more functorial construction for the basic theory of limit linear series, which provides a compactification of the Eisenbud-Harris theory, and shows promise for generalization to…
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Lifting Tropical Intersections
We show that points in the intersection of the tropicaliza- tions of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations…
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DIFFERENTIAL FORMS
Differentials are an important topic in algebraic geometry, allowing the use of some classical geometric arguments in the context of varieties over any field. We will use them to define the genus of…
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Mochizuki's indigenous bundles and Ehrhart polynomials
Mochizuki's work on torally indigenous bundles [1] yields combinatorial identities by degenerating to different curves of the same genus. We rephrase these identities in combinatorial language and…
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Limit linear series moduli stacks in higher rank
In order to prove new existence results in Brill-Noether theory for rank-2 vector bundles with fixed special determinant, we develop foundational definitions and results for limit linear series of…
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Mochizuki's crys-stable bundles: a lexicon and applications
Mochizuki's work on torally crys-stable bundles [18] has extensive implications for the theory of logarithmic connections on vector bundles of rank 2 on curves, once the language is translated…
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Limit linear series for curves not of compact type
  • Brian Osserman
  • Mathematics
    Journal für die reine und angewandte Mathematik…
  • 25 June 2014
We introduce a notion of limit linear series for nodal curves which are not of compact type. We give a construction of a moduli space of limit linear series, which works also in smoothing families,…
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A simple characteristic-free proof of the Brill-Noether theorem
FollowingWelters, we describe howthe use of a different degeneration from that considered by Eisenbud and Harris leads to a simple and characteristic-independent proof of the Brill-Noether theorem…
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On the Solvability of Viewing Graphs
TLDR
This work studies characterizations of “solvable” viewing graphs, and presents several new results that can be applied to determine which pairs of views may be used to recover all camera parameters.
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Linked determinantal loci and limit linear series
We study (a generalization of) the notion of linked determinantal loci recently introduced by the second author, showing that as with classical determinantal loci, they are Cohen-Macaulay whenever…
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