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math.AG1999
Quartic 3-fold: Pfaffians, instantons and half-canonical curves
A. Iliev, D. Markushevich
A generic quartic 3-fold X admits a 7-dimensional family of representations as the Pfaffian of an 8 by 8 skew-symmetric matrix of linear forms. This provides a 7-dimensional moduli…
math.AG1999
Symplectic structure on a moduli space of sheaves on the cubic fourfold
D. Markushevich, A. S. Tikhomirov
A 10-dimensional symplectic moduli space of torsion sheaves on the cubic 4-fold is constructed. It parametrizes the stable rank 2 vector bundles on the hypeplane sections of the cu…
math.AG1999
The Abel-Jacobi map for a cubic threefold and periods of Fano threefolds of degree 14
A. Iliev, D. Markushevich
The Abel-Jacobi maps of the families of elliptic quintics and rational quartics lying on a smooth cubic threefold are studied. It is proved that their generic fiber is the 5-dimens…