Special determinants in higher-rank Brill-Noether theory

Brian Osserman

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arXiv · 1108.4968

Special determinants in higher-rank Brill-Noether theory

Brian Osserman

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Abstract

Continuing our previous study of modified expected dimensions for rank-2 Brill-Noether loci with prescribed special determinants, we introduce a general framework which applies a priori for arbitrary rank, and use it to prove modified expected dimension bounds in several new cases, applying both to rank 2 and to higher rank. The main tool is the introduction of generalized alternating Grassmannians, which are the loci inside Grassmannians corresponding to subspaces which are simultaneously isotropic for a family of multilinear alternating forms on the ambient vector space. In the case of rank 2 with 2-dimensional spaces of sections, we adapt arguments due to Teixidor i Bigas to show that our new modified expected dimensions are in fact sharp.

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Brian Osserman. 2011-08-24. Special determinants in higher-rank Brill-Noether theory. https://arxiv.org/abs/1108.4968

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