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In order to prove new existence results in Brill-Noether theory for rank-2vector bundles with fixed special determinant, we develop foundationaldefinitions and results for limit linear series of higher-rank vector bundles.These include two entirely new constructions of "linked linear series"generalizing earlier work of the author for the classical rank-1 case, as wellas a new canonical stack structure for the previously developed theory due toEisenbud, Harris and Teixidor i Bigas. This last structure is new even in theclassical rank-1 case, and yields the first proper moduli space ofEisenbud-Harris limit linear series for families of curves. We also developresults comparing these three constructions.

Limit linear series moduli stacks in higher rank