arXiv subjects

Rebecca Tramel

Publications and source records attributed to Rebecca Tramel.

3 recordsLinked to original sources

arXiv2018

Bridgeland stability conditions on surfaces with curves of negative self-intersection

Let $X$ be a smooth complex projective variety. In 2002, Bridgeland defined a notion of stability for the objects in $D^b(X)$, the bounded derived category of coherent sheaves on $X$, which generalized the notion of slope stability for vector bundles on curves. There are many nice connections between stability conditions on $X$ and the geometry of the variety. We construct new stability conditions for surfaces containing a curve $C$ whose self-intersection is negative. We show that these stability conditions lie on a wall of the geometric chamber of ${\rm Stab}(X)$, the stability manifold of $X$. We then construct the moduli space $M_σ(\mathcal{O}_X)$ of $σ$-semistable objects of class $[\mathcal{O}_X]$ in $K_0(X)$ after wall-crossing.

math.AG↗

arXiv2017

Diagonal splittings of toric varieties and unimodularity

We use a polyhedral criterion for the existence of diagonal splittings to investigate which toric varieties X are diagonally split. Our results are stated in terms of the vector configuration given by primitive generators of the 1-dimensional cones in the fan defining X. We show, in particular, that X is diagonally split at all q if and only if this configuration is unimodular, and X is not diagonally split at any q if this configuration is not 2-regular. We also study implications for the possibilities for the set of q at which a toric variety X is diagonally split.

math.AG↗

arXiv2014

The genus of projective curves on complete intersection surfaces

We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.

math.AG↗