On the maximum rank of a real binary form
Abstract
We show that a real homogeneous polynomial f(x,y) with distinct roots and degree d greater or equal than 3 has d real roots if and only if for any (a,b) not equal to (0,0) the polynomial af_x+bf_y has d-1 real roots. This answers to a question posed by P. Comon and G. Ottaviani, and shows that the interior part of the locus of degree d binary real binary forms of rank equal to d is given exactly by the forms with d real roots.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2010
- DOI:
- 10.48550/arXiv.1006.5127
- arXiv:
- arXiv:1006.5127
- Bibcode:
- 2010arXiv1006.5127C
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Numerical Analysis
- E-Print:
- To appear in Annali di Matematica Pura ed Applicata