In this paper we study certain algebraic properties of the quantum homology algebra for the class of symplectic toric Fano manifolds. In particular, we examine the semi-simplicity of the quantum homology algebra, and the more general property of containing a field as a direct summand. Our main result provides an easily-verified sufficient condition for… (More)
In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.
Throughout this paper we study the existence of irreducible curves C on smooth projective surfaces Σ with singular points of prescribed topological types S 1 ,. .. , S r. There are necessary conditions for the existence of the type r i=1 µ(S i) ≤ αC 2 + βC.K + γ for some fixed divisor K on Σ and suitable coefficients α, β and γ, and the main sufficient… (More)
Multi-linear secret-sharing schemes are the most common secret-sharing schemes. In these schemes the secret is composed of some field elements and the sharing is done by applying some fixed linear mapping on the field elements of the secret and some randomly chosen field elements. If the secret contains one field element, then the scheme is called linear.… (More)
Characterization of transport and absorption properties of nanofiber webs is a challenge, because in many cases the material is soft and cannot withstand the stresses exerted by the standard instruments. In this paper, we report on development of a new technique for materials characterization. We propose to conduct wicking and permeability experiments for… (More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. Given a smooth family F/Y of geometrically irreducible surfaces, we study sequences of arbitrarily near T-points of F/Y ; they generalize the traditional sequences of infinitely near points of a single smooth surface. We… (More)
Acknowledgements First of all I would like to thank my advisors Joseph Bernstein and Stephen Gelbart for guiding me through this project. I cordially thank Joseph Bernstein for teaching me most of the mathematics I know and for showing me his approach to mathematics and to research in general. I would like to thank my parents, Lena and Ilya for teaching me… (More)
In the current paper we prove the irreducibility of Severi varieties on Hirzebruch surfaces in arbitrary characteristic. Our approach is of purely algebro-geometric nature, and it works in any characteristic. As a result, we obtain a deformation-theoretic proof of the irreducibility of moduli spaces M g in positive characteristic, which does not involve… (More)