Search results for "14H60"
showing 3 items of 3 documents
The Coble Quadric
2023
Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the Coble quartic. Gruson, Sam and Weyman realized that this quartic could be constructed from a general skew-symmetric fourform in eight variables. Using the lines contained in the quartic, we prove that a similar construction allows to recover SU$_C(2, L)$, the moduli space of rank two stable vector bundles on C with fixed determinant of odd degree L, as a subvariety of $G(2, 8)$. In fact, each point $p \in C$ defines a natural embedding of SU$_C(2, \mathca…
Maximal Cohen-Macaulay Modules over the Affine Cone of the Simple Node
2005
A concrete description of all graded maximal Cohen-Macaulay modules of rank one and two over the affine cone of the simple node (a non-isolated singularity) is given. For this purpose we construct an alghoritm that provides extensions of MCM modules over an arbitrary hypersurface.
On a question of Mehta and Pauly
2013
In this short note we provide explicit examples in characteristic $p$ on certain smooth projective curves where for a given semistable vector bundle $\mathcal{E}$ the length of the Harder-Narasimhan filtration of $F^\ast \mathcal{E}$ is longer than $p$. This answers a question of Mehta and Pauly raised in arXiv:math/0607565.