#### Alladi Ramakrishnan Hall

#### Classification of obstructed bundles over a very general sextic surface using Alexander-Hirschowitz Theorem and Mestrano-Simpson Conjecture

#### Sarbeswar Pal,

##### IISER, TVM

*Let $S$ be a very general sextic surface over complex numbers.*

Let $\mathcal{M}(H, c_2)$ be the moduli space of rank $2$ stable bundles

on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In

this talk we will introduce a new approach using Alexander-Hirschowitz

Theorem to give a bound of the space of obstructions of a point $E \in

\mathcal{M}(H, c_2)$ and we will apply this to proof Mestrano -Simpson

conjecture on number of irreducible components of $\mathcal{M}(H, 11)$.

Done