activity
20132026
most citedRational cuspidal curves on del-Pezzo surfaces

6 citations · 9 across the 4 of their papers we have counts for

collaborators

7 papers

math.GT2026

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…

math.GT2021

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…

math.GT2016

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…

math.AG2016

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 …

math.AG2015★ 6 cited

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…

math.GT2013

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…

math.AG2013★ 3 cited

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…