arXiv subjects

Roshan Tajarod

Publications and source records attributed to Roshan Tajarod.

4 recordsLinked to original sources

arXiv2025

Rationality and categorical properties of the moduli of instanton bundles on the projective 3-space

We prove the rationality and irreducibility of the moduli space of mathematical instanton vector bundles of arbitrary rank and charge on $\mathbb P^3$. In particular, the result applies to the rank-2 case. This problem was first studied by Barth, Ellingsrud-Stromme, Hartshorne, Hirschowitz-Narasimhan in the late 1970s. We also show that the mathematical instantons of variable rank and charge form a monoidal category. The proof is based on an in-depth analysis of the Barth-Hulek monad-construction and on a detailed description of the moduli space of (framed and unframed) stable bundles on Hirzebruch surfaces.

math.AG↗

arXiv2019

On the rationality of the moduli space of instanton bundles on the projective 3-space

We prove the rationality and irreducibility of the moduli space of---what we call---the endomorphism-general instanton vector bundles of arbitrary rank on the projective space. In particular, we deduce the rationality of the moduli spaces of rank-two mathematical instantons. This problem was first studied by Hartshorne, Hirschowitz-Narasimhan in the late 1970s, and it has been reiterated within the framework of the ICM 2018.

math.AG↗

arXiv2015

On the $q$-ampleness of the tensor product of two line bundles

We prove that the tensor product of two line bundles, one being $q$-ample and the other with sufficiently low-dimensional base locus, is still $q$-ample.

math.AG↗

arXiv2015

About the cohomological dimension of certain stratified varieties

We determine an upper bound for the cohomological dimension of the complement of a closed subset in a projective variety which possesses an appropriate stratification. We apply the result to several particular cases, including the Bialynicki-Birula stratification; in this latter case, the bound is optimal.

math.AG↗