6 citations · 9 across the 4 of their papers we have counts for
7 papers
Real rational knots in the quadric of signature~
Shane D'Mello, Priya Rani
We study the space of real rational curves of low degree in the quadric of signature and provides a classificaton of real rational knots and nodal curves. Apart from the cl…
Properties of glued knots
Shane D'Mello, Vinay Gaba
We study the properties of glued knots, a sub-class of real rational knots, that can be constructed by gluing ellipses. We define an invariant called the gluing degree and relate i…
Constructing real rational knots by gluing
Shane D'Mello, Rama Mishra
We show that the problem of constructing a real rational knot of a reasonably low degree can be reduced to an algebraic problem involving the pure braid group: expressing an associ…
M-curves and symmetric products
Indranil Biswas, Shane D'Mello
Let be a geometrically irreducible smooth projective M-curve of genus defined over the field of real numbers. We prove that the -th symmetric product of …
Rational cuspidal curves on del-Pezzo surfaces
Indranil Biswas, Shane D'Mello, Ritwik Mukherjee +1
We obtain an explicit formula for the number of rational cuspidal curves of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the s…
Classification of real rational knots of low degree in the 3-sphere
Shane D'Mello
In this paper we classify, up to rigid isotopy, non-singular real rational curves of degrees less than or equal to 6 in a quadric homeomorphic to the 3-sphere. We also study their…
Rigid isotopy classification of real degree-4 planar rational curves with only real nodes (An elementary approach)
Shane D'Mello
We prove an elementary method to classify, up to rigid isotopy, all nodal degree 4 real rational curves in that have only real double points. We show how to associa…