Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Alexandr Tikhomirov
Affiliation:

HSE Moscow
Date:

Tue, 2019-02-19 14:00 - 15:00 In this talk, we will give an overview of recent results on the geography and geometry of the Gieseker-Maruyama

moduli scheme $M = M(c_1,c_2,c_3)$ of rank 2 stable coherent sheaves with first Chern class $c_1 = 0$ or $-1$,

second Chern class $c_2$, and third Chern class $c_3\ge0$ on the projective space $\mathbb{P}^3$.

We will enumerate all currently known irreducible components of $M$ for small values of $c_2$ and $c_3\ge0$.

We then present the constructions of new series of components of $M$ for arbitrary $c_2$. The problem of

connectedness of $M$ will be discussed. These are the resuts of several joint works of the speaker with

M.Jardim, D.Markushevich, A.Ivanov, C.Almeida and others.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/5312