Prym differentials, multiplicative functions, Prym's and Gunning's vector bundle over Teichmueller space and over space of kleinian groups,Jacobi varieties, Riemann's theta-function, monodromy groups.
Subject:
The commutative diagram of topological covering mappings,where the Teichmueller space is universal covering over space of compact Riemann surfaces with incomplete marking and over space of Koebe groups, was constructed. The general theory of Prym differential and of multiplicative functions on variable compact Riemann surfaces for arbitrary characters for compact surface was constructed. Two-sided estimates for number of multiplicative Weierstrass points was obtained. New method study of multiplicative Weierstrass points, multiplicative Weierstrass gaps and multiplicative Noether gaps with the help of special filtrations in the Jacobi manifold was proposed. The Prym's vector bundle and the Gunning's vector bundle real- analytic isomorphically over product Teichmueller space and space of nontrivial normed characters was proved. The big class of matrix representations for the Torelli group was obtained. Exact variational formula for monodromy groups linear differential equation two order on compact Riemann surface was finded.
Biography
Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University in 1973 (department of theory function). Ph.D. thesis was defended in 1979. A list of my works contains more than 30 titles.
Main publications:
Chueshev V. V. Prostranstva kompaktnykh rimanovykh poverkhnostei i grupp Kebe // Sib. matem. zhurn., 1981, t. 22, # 5, s. 190–205.
Chueshev V. V. Tochnaya variatsionnaya formula dlya gruppy monodromii na kompaktnoi rimanovoi poverkhnosti // Mezhvuz. sb. nauch. trudov, posvyasch. 100-letiyu N. N. Luzina, Kemerovo, KemGU, s. 23–28.
Chueshev V. V. Kogomologicheskoe rassloenie Ganninga i gruppa Torelli, Sib. matem. zhurn., 1990, t. 31, # 3, s. 198–203.
Chueshev V. V. Vektornye rassloeniya Prima i Ganninga nad prostranstvom Teikhmyullera // Sib. matem. zhurn., 2001, t. 42, # 4, s. 937–951.
Chueshev V. V. Periody garmonicheskikh differentsialov Prima na kompaktnykh rimanovykh poverkhnostyakh // Sib. matem. zhurn., 2002, t. 43, # 4, s. 212–231.
Alexander V. Chueshev, Victor V. Chueshev, “Variational formulas of the monodromy group for a third-order equation on a compact Riemann surface”, J. Sib. Fed. Univ. Math. Phys., 15:3 (2022), 308–318
2019
2.
Alexander V. Chueshev, Victor V. Chueshev, “Vector bundle of prym differentials over Teichmüller spaces of surfaces with punctures”, J. Sib. Fed. Univ. Math. Phys., 12:3 (2019), 263–275
2018
3.
Alexander V. Chueshev, Victor V. Chueshev, “Prym differentials and Teichmüller spaces”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 686–691
2016
4.
T. S. Krepizina, V. V. Chueshev, “Prym differentials on variable torus”, Sib. J. Pure and Appl. Math., 16:3 (2016), 40–54; J. Math. Sci., 230:1 (2018), 79–94
2014
5.
M. I. Tulina, V. V. Chueshev, “Prym Differentials on a Variable Compact Riemann Surface”, Mat. Zametki, 95:3 (2014), 457–474; Math. Notes, 95:3 (2014), 418–433
T. A. Pushkareva, V. V. Chueshev, “The space of harmonic Prym differentials on a variable compact Riemann surface”, Sibirsk. Mat. Zh., 55:2 (2014), 379–395; Siberian Math. J., 55:2 (2014), 309–322
A. A. Kazantseva, V. V. Chueshev, “The spaces of meromorphic Prym differentials on a finite Riemann surface”, Sibirsk. Mat. Zh., 53:1 (2012), 89–106; Siberian Math. J., 53:1 (2012), 72–86
T. S. Krepitsina, V. V. Chueshev, “Multiplicative functions and Prym differentials on variable torus”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:1 (2012), 74–90; J. Math. Sci., 198:5 (2014), 546–563
Alena A. Bespomestnych, Victor V. Chueshev, “Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces”, J. Sib. Fed. Univ. Math. Phys., 2:1 (2009), 31–40
10.
A. N. Chichkakova, V. V. Chueshev, “Univalent Meromorphic Differentials on Riemann Surfaces of Types $(g,n)$”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 9:1 (2009), 73–84
2008
11.
Anna N. Chichkakova, Viktor V. Chueshev, “Prym Differentials on a Finite Riemann Surface”, J. Sib. Fed. Univ. Math. Phys., 1:3 (2008), 335–347
2004
12.
V. V. Chueshev, “An Explicit Variational Formula for the Monodromy Group”, Mat. Tr., 7:2 (2004), 126–158; Siberian Adv. Math., 15:2 (2005), 1–32
V. V. Chueshev, “Multiplicative Weierstrass Points and the Jacobi Variety of a Compact Riemann Surface”, Mat. Zametki, 74:4 (2003), 629–636; Math. Notes, 74:4 (2003), 593–598
V. V. Chueshev, E. Yakubov, “Weierstrass multiplicative points on a compact Riemann surface”, Sibirsk. Mat. Zh., 43:6 (2002), 1408–1429; Siberian Math. J., 43:6 (2002), 1141–1158
V. V. Chueshev, “Periods of harmonic Prym differentials on a compact Riemann surface”, Sibirsk. Mat. Zh., 43:4 (2002), 937–952; Siberian Math. J., 43:4 (2002), 756–768
2001
16.
V. V. Chueshev, “The Prym vector bundle and Gunning vector bundle over the Teichmüller space”, Sibirsk. Mat. Zh., 42:4 (2001), 937–951; Siberian Math. J., 42:4 (2001), 789–800
V. V. Chueshev, “Harmonic and holomorphic Prym differentials on a compact Riemann surface”, Sibirsk. Mat. Zh., 40:2 (1999), 465–475; Siberian Math. J., 40:2 (1999), 402–411
1990
18.
V. V. Chueshev, “Cohomological Gunning fibration and the Torelli group”, Sibirsk. Mat. Zh., 31:3 (1990), 198–203; Siberian Math. J., 31:3 (1990), 523–527
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