Abstract:
Let $L$ be a linear bundle on a smooth projective curve and consider the
natural rational map from the extension space $\mathbb{P}_L =
\mathbb{P}(Ext^1(L,\mathcal{O}))$ to the moduli space
$M_{2,L}$ of vector bundles of rank $2$ with determinant $L$. Following
Bertram's '92 paper I will construct a new variety
$\widetilde{\mathbb{P}_L}$ with a sequence of blow-ups and a morphism to
$M_{2,L}$, which allow to calculate dimensions of global sections of
linear bundles on $M_{2,L}$ and answer some other questions on geometry
of the moduli spaces.
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