21 citations · 21 across the 5 of their papers we have counts for
5 papers
Random fields and the enumerative geometry of lines on real and complex hypersurfaces
Saugata Basu, Antonio Lerario, Erik Lundberg +1
We derive a formula expressing the average number of real lines on a random hypersurface of degree in in terms of the expected modulus of the…
Bounds on the individual Betti numbers of complex varieties, stability and algorithms
Saugata Basu, Cordian Riener
We prove graded bounds on the individual Betti numbers of affine and projective complex varieties. In particular, we give for each , explicit bounds on the -th Betti numb…
Algorithms in Real Algebraic Geometry: A Survey
Saugata Basu
We survey both old and new developments in the theory of algorithms in real algebraic geometry -- starting from effective quantifier elimination in the first order theory of reals…
Toric cubes are closed balls
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
We prove that toric cubes, which are images of under monomial maps, are the closures of graphs of monotone maps, and in particular semi-algebraically homeomorphic to clos…
Semi-monotone sets
Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov
A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the rea…