papers by Andrei Tyurin (English and Russian)

(partial!)

Статьи Андрея Тюрина на сайте mathnet.ru, напечатанные по-русски (с PDF)

== Papers in Russian (частичный список!) ==

• • О классификации двумерных алгебраических расслоений над алгебраической кривой произвольного рода, 1964

  • Классификация векторных расслоений над алгебраической кривой произвольного рода, 1965

  • О классификации n-мерных векторных расслоений над алгебраической кривой произвольного рода, 1966 (будет добавлена позже)

  • Геометрия модулей векторных расслоений (1974)

  • О пересечении квадрик, 1975 (будет добавлена позже)

    • Периоды и главные части квадратичных дифференциалов (1978)

  • Особенности общей квадратичной формы (1980).

  • Алгебро-геометрические аспекты гладкости. Полиномы Дональдсона. (1989)

== Papers in English (partial list!) ==

• 1969: Analogs of Torelli theorem for rank 2 vector bundles on curves.

• Fano surface of a cubic threefold in P^4 (1970)

• A Fano surface of a 3-dimensional cubic in P^4 and Torelli theorem (1970)

• 1972: Singularities of theta-divisor of a Picard variety of Fano surface for cubic in P^4

• Geometry of Theta Divisor of a Prym variety (1975)

• An Invariant of a bundle of quadrics (1975)

• Periods and Principal parts of quadratic differentials (1977).

• Superposition of instantons (1982)

• Local and global invariants of a 4-dimensional Riemannian manifold (1985)

• Special 0-cycles on a K3 surface (1987)

• Cycles, curves and vector bundles on algebraic surfaces (1987).

• 1990: The moduli spaces of vector bundles on threefolds, surfaces and curves I. Preprint: Erlangen, 1990. It is in the collected works, volume 1, page 176. Will be linked later.

• On the Weil-Petersson metric on the moduli space of vector bundles on a surface (1991)

• Almost canonical polynomials of algebraic surface (1992).

• Canonical Spin polynomials of an algebraic surface(1994) (part 2) (part 3)

• 1994: A. Tikhomirov and A. Tyurin. "Application of geometric

• approximation procedure to computing the Donaldson polynomials for CP2". (MISSING!) Mathematica Goettingensis, Sonderforschungsbereichs ”Geometry and Analysis”. 1994, Heft 12, 1 – 71.

• Canonical and almost canonical spin polynomials of an algebraic surface, 1995 (will be linked later)

• 1995: Classical geometry of vector bundles

  • • Preprints

• • Abelian Lagrangian algebraic geometry (with Alexei Gorodentsev)

    • 1999 version

    • 2001 version

  • Non-abelian Analog's of Abel's Theorem

  • English version, 2000 (PostScript)

  • another English version, translated from Russian (2001)

  • Russian version, 2000 -- to be posted

  • Comments on Chern-Simons theory (dvi)

  • Part 2: complex case (dvi)

Books

• Quantization, Classical and Quantum Field Theory and Theta-Functions. (2003)

• Collected works (Russian, 3 volumes)

• Collected works, English:

• Volume 1

Papers in the Arxive

1. math.AG/0302249: Hitchin systems on ll-curves

2. math.AG/0302101: Fano versus Calabi - Yau

3. math.AG/0210466 : Quantization, Classical and Quantum Field Theory and Theta - Functions

4. math.AG/0210135: On the Mumford - Narasimhan problem

5. math.AG/0105216 : Delzant models of moduli spaces

6. math.DG/0102118 : Lattice gauge theories and the Florentino conjecture

7. math.DG/0011035 : Three mathematical faces of SU(2) - spin networks

8. math.AG/9909094 : Complexification of Bohr-Sommerfeld conditions

9. math.AG/9909084 : On Bohr-Sommerfeld bases

10. math.AG/9904046 : Quantization and ``theta functions''

11. math.AG/9902027 : Geometric quantization and mirror symmetry

12. math.AG/9806006 : Special Lagrangian geometry and slightly deformed algebraic geometry (spLag and sdAG)

13. dg-ga/9507004 : Localisation of the Donaldson's invariants along Seiberg-Witten classes joint with Victor Pidstrigach

14. alg-geom/9406002: Spin canonical invariants of 4-manifolds and algebraic surfaces

15. alg-geom/9210003: The simple method of distinguishing the underlying differentiable structures of algebraic surfaces

Obituary -- by Bogomolov et al.