MANDAL-DISSERTATION-2020.pdf (812.15 kB)

On Restricted Tangent Bundles of Grassmannian, and Betti Numbers of The moduli of Stable Sheaves on P^2

thesis
posted on 01.05.2020, 00:00 by Sayanta Mandal
This thesis is based on work done on two different problems. The first problem is regarding restricted tangent bundles of the Grassmannian to rational curves. Let n >= 4, 2 <= r <= n-2 and e >= 1. We show that the intersection of the locus of degree e morphisms from P^1 to G(r, n) with the restricted universal sub-bundles having a given splitting type and the locus of degree e morphisms with the restricted universal quotient-bundle having a given splitting type is non-empty and generically transverse. As a consequence, we get that the locus of degree e morphisms from P^1 to G(r, n) with the restricted tangent bundle having a given splitting type need not always be irreducible. The second problem is regarding the Betti numbers of the moduli space of sheaves on the projective plane. Let r >= 2 be an integer, and let a be an integer coprime to r. We show that if c_2 >= n+ (r-1)a^2 /2r + (r^2 + 1)/2 , then the 2nth Betti number of the moduli space M_{P^2,O_{P^2} (1)}(r,O_{P^2}(a), c_2) stabilizes.

Coskun, Izzet

Coskun, Izzet

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Doctoral

Degree name

PhD, Doctor of Philosophy

Committee Member

Ein, Lawrence Tucker, Kevin Zhang, Wenliang Riedl, Eric

May 2020

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