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Linear stability and rank two Clifford indices of algebraic curves with applications
Ali Bajravani, Angela Ortega
We prove that any vector bundle computing the rank-two Clifford index of a smooth projective algebraic curve is linearly semistable. We also identify conditions under which such bu…
Martens and Mumford theorems for higher rank Brill--Noether loci
Parviz Asefi Nazarlou, Ali Bajravani, George H. Hitching
Generalizing the Martens theorem for line bundles over a curve , we obtain upper bounds on the dimension of the Brill--Noether locus parametrizing stable bundles of…
Excess dimensions of Brill--Noether schemes of rank two stable bundles
Ali Bajravani
We use results of M. Aprodu and E. Sernesi to extend a result by Fulton--Harris--Lazarsfeld in Brill--Noether theory of line bundles %and, as well, a result by Aprod-Sernesi in the…
Brill--Noether loci on moduli spaces of symplectic bundles over curves
Ali Bajravani, George H. Hitching
The symplectic Brill--Noether locus associated to a curve parametrises stable rank bundles over with at least sections and which carry a n…
Bounds on the Dimension of the Brill-Noether Schemes of Rank Two Bundles
Ali Bajravani
The aim of this note is to find upper bounds on the dimension of Brill-Noether locus' inside the moduli space of rank two vector bundles on a smooth algebraic curve. We deduce some…
A note on the Tangent Cones of the scheme of Secant Loci
Ali Bajravani
The point of this short note concerns with two facts on the scheme of secant loci. The first one is an attempt to describe the tangent cone of these schemes globally and the second…