7 papers
Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7
A. Iliev, D. Markushevich
According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). It is proven that the moduli…
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…
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…
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…
The Abel-Jacobi map of a moduli component of vector bundles on the cubic threefold
D. Markushevich, A. S. Tikhomirov
The Abel-Jacobi map of the family of elliptic quintics lying on a general cubic threefold is studied. It is proved that it factors through a moduli component of stable rank 2 vecto…
Exceptional quotient singularities
D. Markushevich, Yu. G. Prokhorov
A singularity is said to be exceptional (in the sense of V. Shokurov), if for any log canonical boundary, there is at most one exceptional divisor of discrepancy -1. In our previou…