# Fedor L. Zak

Leading Researcher, Doctor of Sciences in Mathematics**E-mail:**
zak (at) mccme.ru

## Selected Publications

*(Links
lead to full texts of papers in pdf format)*

### Mathematical Economics

"Taxation in Walrasian economy", 2009.

"Stability of economic equilibrium", 181-216, Russian contributions to game theory and equilibrium theory, Game theory, mathematical programming and operations research 39, Springer, 2006.

"Sales tax and economic equilibrium", Moscow, CEMI, 1993 (in Russian).

"Inflation as a means for balancing the market in mixed economies", Moscow, CEMI, 1991 (in Russian).

"Taxation in Walrasian economy", ESEM-1991, Cambridge.

"Rationing and market", ESEM-1989, Augsburg.

"Mechanism of reselling of centralized resources at flexible prices: structure and stability of equilibria", Moscow, CEMI, 1987 (in Russian).

"Economic equilibrium and stability of price adjustment", Category of social utility: problems of methodology and structurization, 51-90, Moscow, CEMI, 1983 (in Russian).

"Stability of economic equilibrium", Methods of the theory of extremal problems in economics (V.L. Levin, ed.), 72-106, Moscow, Nauka, 1981 (in Russian).

### Algebraic Geometry

"Topological structure of real and complex algebraic varieties" (with V. Kharlamov).

"Asymptotic behaviour of numerical invariants of algebraic varieties", 16 pp., submitted to J. European Math. Soc.

"Castelnuovo bounds for higher dimensional varieties", 53 pp., submitted to Ann. Math.

"Determinants of projective varieties and their degrees", pp. 206-238 in: Algebraic Transformation Groups and Algebraic Varieties, Encyclopaedia of Mathematical Sciences, vol. 132, Subseries Invariant Theory and Algebraic Transformation Groups, vol. III, Springer-Verlag, Berlin-Heidelberg-New York, 2004.

"Projective invariants of quadratic embeddings", Math. Ann. 313(1999), 507-545.

"Elementary projective geometry" (Notes by Enrico Rogora), pp. 90-120, Projective Varieties, Linear Systems, and Vector Bundles, Istituto Nazionale di Alta Matematica "F. Severi", Roma, 1994.

"Varieties of codegree three in projective space", Geometry of complex projective varieties, 302-320, Mediterranean Press, 1993.

"Tangents and secants of algebraic varieties", 175 pp., Amer. Math. Soc., Providence, 1993.

"Some properties of dual varieties and their applications in projective geometry", Lecture Notes in Math. 1479(1991), 273-282.

"Theorems on tangency for subvarieties of complex tori", Mat. Zametki 43 (1988), ¹3, 382-392 (in Russian); English translation: Math. Notes 43, no.3, 219-225.

"Structure of Gauss maps", Funkc. Analiz i ego Prilozh. 21 (1987), ¹1, 39-50 (in Russian); English translation: Func. Anal. Appl. 21, no.1, 32-41.

"Linear systems
of hyperplane sections on varieties of small codimension", Funkc. Analiz
i ego Prilozh. 19(1985), ¹3, 1-10; English
translation: Func. Anal. Appl. 19, no.3, 165-173.

"Severi varieties", Mat. Sbornik 126 (1985), 115-132 (in Russian); English translation: Math. USSR Sbornik 54(1986), no.1, 113-127.

"Varieties of small codimension arising from group actions", Addendum to: R. Lazarsfeld and A. Van de Ven, Topics in the geometry of projective space. Recent work of F.L. Zak, Birkhauser, 1984, 41 -52.

"Projections of algebraic varieties", Mat. Sbornik 116 (1981), 593-602 (in Russian); English translation: Math. USSR Sbornik 44(1983), no.4, 535-544.

"Deformations of modifications of algebraic spaces", Mat. Sbornik 96 (1975), ¹2, 212-239 (in Russian); English translation: Math. USSR Sbornik 25(1975), no.2, 199-223.

"q-finite morphisms in formal algebraic geometry", Izvestiya AN SSSR, ser. mat. 39(1975), ¹1, 28-66 (in Russian); English translation: Math. USSR Izvestija 9 (1975), no.1, 27-62.

"On stability of birational morphisms", Uspekhi mat. nauk 29(1974), ¹4, 165-166 (in Russian); English translation: Russian Math. Surveys.

"On stability of birational morphisms", Uspekhi mat. nauk 29(1974), ¹4, 165-166 (in Russian); English translation: Math. Notes 13(1973), 520-525.