9 citations · 41 across the 15 of their papers we have counts for
18 papers
Breaking the symmetry in excess intersection and counting solutions of systems of polynomials
Pinaki Mondal
We revisit the fundamental problem of assigning intersection multiplicities to subsets of solutions of (square) systems of polynomials. Severi [Ann. Mat. Pura Appl. 26 (4), 1947] s…
How many zeroes? Counting the number of solutions of systems of polynomials via geometry at infinity (Draft III)
Pinaki Mondal
In this book we describe an approach through toric geometry to the following problem: "estimate the number (counted with appropriate multiplicity) of isolated solutions of n polyno…
Normal equivariant compactifications of G^2_a with Picard number one
Pinaki Mondal
We classify all normal G^2_a-surfaces with Picard number one, and characterize which of these surfaces have at worst log canonical, and which have at worst log terminal singulariti…
Intersection multiplicity, Milnor number and Bernstein's theorem
Pinaki Mondal
We explicitly characterize when the Milnor number at the origin of a polynomial or power series (over an algebraically closed field k of arbitrary characteristic) is the minimum of…
Algebraicity of normal analytic compactifications of C^2 with one irreducible curve at infinity
Pinaki Mondal
We present an effective criterion to determine if a normal analytic compactification of C^2 with one irreducible curve at infinity is algebraic or not. As a by product we establish…
Mori dream surfaces associated with curves with one place at infinity
Pinaki Mondal
We study a class of rational surfaces (considered in [Campillo, Piltant and Reguera, 2005]) associated to curves with one place at infinity and explicitly describe generators of th…