Topological Invariants of Universal Vector Bundles on Moduli Spaces of Coherent Sheaves on $\mathbb P_2$

Student: Statnik Evgeny

Educational Programme: Mathematics (Bachelor)

Final Grade: 9

Year of Graduation: 2016

A geometrical description of the moduli space $\mathfrak M$ of rank $2$ stable torsion-free coherent sheaves with $c_1=-1$ and $c_2=k$ on the projective plane $\mathbb{CP}^2$ is given. We consider some methods for calculating the top Chern class of the universal vector bundle $\mathcal G^{\oplus 4}$, where fiber of $\mathcal G$ over a point that represents a sheaf $F$ is the first cohomology $H^1(F, \mathbb {CP}^2)$. The bundle $\mathcal G^{\oplus 4}$ is interesting because of $S$-duality, which predicts certain modular properties of the generating function for the top Chern classes in question.

Full text (added June 6, 2016)

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