arXiv subjects

Anna Kazanova

Publications and source records attributed to Anna Kazanova.

3 recordsLinked to original sources

arXiv2016

Scaling of conformal blocks and generalized theta functions over $\bar{M}_{g,n}$

By way of intersection theory on $\bar M_{g,n}$, we show that geometric interpretations for conformal blocks, as sections of ample line bundles over projective varieties, do not have to hold at points on the boundary. We show such a translation would imply certain recursion relations for first Chern classes of these bundles. While recursions can fail, geometric interpretations are shown to hold under certain conditions.

math.AG↗

arXiv2014

On $S_n$-invariant conformal blocks vector bundles of rank one on $\overline M_{0,n}$

For any simple Lie algebra, a positive integer, and tuple of compatible weights, the conformal blocks bundle is a globally generated vector bundle on the moduli space of pointed rational curves. We classify all $S_n$-invariant vector bundles of conformal blocks for $\mathfrak{sl}_n$ which have rank one. We show that the cone generated by their base point free first Chern classes is polyhedral, generated by level one divisors.

math.AG↗

arXiv2014

Degenerations of Godeaux surfaces and exceptional vector bundles

A recent construction of Hacking relates the classification of stable vector bundles on a surface of general type with $p_g = 0$ and the boundary of the moduli space of deformations of the surface. In the present paper we analyze this relation for Godeaux surfaces. We provide a description of certain boundary components of the moduli space of Godeaux surfaces. Also we explicitly construct certain exceptional vector bundles of rank 2 on Godeaux surfaces, stable with respect to the canonical class, and examine the correspondence between the boundary components and such exceptional vector bundles.

math.AG↗