On intersections of symmetric determinantal varieties and theta characteristics of canonical curves
Abstract
From a blockdiagonal $(n+1) \times (m+1) \times (m+1)$ tensor symmetric in the last two entries one obtains two varieties: an intersection of symmetric determinantal hypersurfaces $X$ in $n$dimensional projective space, and an intersection of quadrics $\mathfrak{C}$ in $m$dimensional projective space. Under mild technical assumptions, we characterize the accidental singularities of $X$ in terms of $\mathfrak{C}$. We apply our methods to algebraic curves and show how to construct theta characteristics of certain canonical curves of genera 3, 4, and 5, generalizing a classical construction of Cayley.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.08740
 Bibcode:
 2021arXiv210908740K
 Keywords:

 Mathematics  Algebraic Geometry;
 14M12 (primary);
 14H10 (secondary)
 EPrint:
 32 pages. Comments welcome!