Semiorthogonal Decompositions on Enriques Surfaces and Derived Torelli Theorem
We show that the general Enriques surface can be recovered from the Kuznetsov component of its bounded derived category of coherent sheaves.
math.AG↗
arXiv subjects
Giorgio Scattareggia
Publications and source records attributed to Giorgio Scattareggia.
A perfect obstruction theory for moduli of coherent systems
Let $C$ be a curve of genus $g$. A coherent system on $C$ is a pair $(E,V)$, where $E$ is a finite rank vector bundle on $C$ and $V$ is a linear subspace of the space of global sections of $E$. The type of a coherent system $(E,V)$ is a triple $(n,d,k)$, where $n$ is the rank of $E$, $d$ is the degree of $E$ and $k$ is the dimension of $V$. The notion of stability for a coherent system $(E,V)$ differs from the stability of the bundle $E$ and depends on the choice of a real parameter $α$. The moduli space of $α$-stable coherent systems of type $(n,d,k)$ has an expected dimension $β= β(n,d,k)$ which depends on the genus of the curve $C$ and on the type of the coherent systems. We construct a perfect obstruction theory for the moduli spaces of $α$-stable coherent systems which has rank equal to the expected dimension $β$. In our construction we do not fix one curve, but we work on families of Gorenstein projective curves.
math.AG↗