Birational models for moduli of quartic rational curves
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Abstract
We study the geometry of the moduli space M_4(P^4) of rational normal curves of degree 4 and its compactifications in the Hilbert scheme Hilb^{4n+1}(P^4), in the moduli space of Kronecker modules of type (4,2) and in the moduli space M^{4n+2}(P^4) of semi-stable sheaves on P^4 with Hilbert polynomial 4n+2.
This project is motivated by the work of Ch. Lehn, M. Lehn, Ch. Sorger and D. van Straten, who constructed a family of holomorphic symplectic manifolds via a contraction of the moduli space M_3(Y) of rational curves on a smooth cubic fourfold that does not contain a plane.