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- Ilya Tyomkin
- 2006

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.

- THOMAS KEILEN, ILYA TYOMKIN
- 2001

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)

- Ilya TYOMKIN
- 2011

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)

- Ilya TYOMKIN
- 2009

We study sequences of infinitely near T-points of a smooth family F/Y of geometrically irreducible surfaces. We destinguish a special sort of such sequences, the strict sequences. To each one, we associate an ordered unweighted Enriques diagram. We prove that the various sequences with a given diagram form a functor, and we represent it by a smooth… (More)

- Ilya Tyomkin
- 2004

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)

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