In mathematics, the Gauss–Manin connection is a connection on a certain vector bundle over a base space S of a family of algebraic varieties V s {\displaystyle...

equations. The Gauss–Manin connection is a basic ingredient of the study of cohomology in families of algebraic varieties. He developed the Manin obstruction...

higher dimensions Gauss's braid in braid theory – a four-strand braid Gauss–Codazzi equations Gauss–Manin connection, a connection on a vector bundle...

one can consider the isomonodromy equations as nonhomogeneous Gauss–Manin connections. This leads to alternative descriptions of the isomonodromy equations...

Kodaira–Spencer map and the Bogomolev-Tian-Todorov theorem) there is the Gauss-Manin connection ∇ θ {\displaystyle \nabla _{\theta }} taking a ( p , q ) {\displaystyle...

necessarily be defined for non-flat connections. The Gauss–Manin connection is a prominent example of a connection whose horizontal sections are studied...

Edge-of-the-wedge theorem FBI transform Localization of a ring Vanishing cycle Gauss–Manin connection Differential algebra Perverse sheaf Mikio Sato Masaki Kashiwara...

Mochizuki (2002a) he pointed out that arithmetic Kodaira–Spencer map and Gauss–Manin connection may give some important hints for Vojta's conjecture, ABC conjecture...

Katz for Picard–Fuchs equations (in the contemporary sense of the Gauss–Manin connection), as amplified in the Tannakian direction by André. It also applies...

been shown to be a very special case of a general phenomenon, the Gauss–Manin connection. Schnell, Christian, On Computing Picard-Fuchs Equations (PDF) J...

the Malcev algebra Yuri Manin, author of the Gauss–Manin connection in algebraic geometry, Manin-Mumford conjecture and Manin obstruction in diophantine...

team), Olympic champion (2000), heart attack. Yuri Manin, 85, Russian mathematician (Gauss–Manin connection). John L. Meisenheimer, 89, American chemist. Zinaid...

the Malcev algebra Yuri Manin, author of the Gauss–Manin connection in algebraic geometry, Manin-Mumford conjecture and Manin obstruction in diophantine...

number theory Mathematical constant L-function Jacobian variety Gauss–Manin connection Mixed motives (math) Tannakian formalism Weisstein, Eric W. "Algebraic...

fractal, Lyapunov time Yuri Manin, author of the Gauss–Manin connection in algebraic geometry, Manin-Mumford conjecture and Manin obstruction in diophantine...

torus orbifolds". arXiv:2006.00495 [math.KT]. Yashinski, Allan (2012). "The Gauss-Manin connection and noncommutative tori". arXiv:1210.4531 [math.KT]....

sentences for many types of offences. Born: Yuri Manin, Russian mathematician known for the Gauss–Manin connection; in Simferopol, Crimean ASSR, Soviet Union...

MR 2338364. p. 545 Movasati, Hossein; Nikdelan, Younes (2021-09-01). "Gauss-Manin Connection in Disguise: Dwork Family". Journal of Differential Geometry. 119...

_{X}^{1}} is the sheaf of 1-forms on X. This natural flat connection is a Gauss–Manin connection ∇ and can be described by the Picard–Fuchs equation. A variation...

theorem characteristic linear system of an algebraic family of curves Gauss–Manin connection Derived category Ext functor Kodaira (2005). Complex Manifolds and...

generalization of the Gauss–Manin connection constructed in a manner analogous to that in which the Ehresmann connection generalizes the Koszul connection. The construction...

Knizhnik–Zamolodchikov equations (or, KZ equations) with a suitable Gauss–Manin connection and constructed multidimensional hypergeometric solutions of the...

Mathematical Society. pp. 199–205. ISBN 0-8218-2040-0. OCLC 48892689. Milnor number Hodge structure Kodaira–Spencer map Gauss–Manin connection Unfolding...

Aleksandr Kharchikov, 73, folk singer-songwriter. Yuri Manin, 85, mathematician (Gauss–Manin connection). 8 January Aleksandr Shabanov, 87, chemist and politician...

Cohen: Cohen, Daniel C.; Orlik, Peter (2005). "Gauss–Manin connections for arrangements, III Formal connections". Transactions of the American Mathematical...

been the main objects of study for the better part of the 20th century. Manin–Drinfeld theorem Moduli stack of elliptic curves Modularity theorem Shimura...

Cambridge University Press, 1910, reprinted by Dover, NY, 1964, pp. 144–145 Manin & Panchishkin 2007, p. 341 Singh, pp. 62–66 Singh, p. 67 Aczel 1996, p. 10...

^{k_{1}+k_{2}}(V)\right).} It can be verified (as is done by Kostrikin and Manin) that the resulting product is in fact commutative and associative. In some...

d'Enfants (L. Schneps ed.), London Math. Soc. Lecture Note Ser, 200, 115-145. Manin YI (2004). Real multiplication and noncommutative geometry (ein Alterstraum)...

entries are elements of Z 2 {\displaystyle \mathbb {Z} _{2}} -graded rings). Manin matrices form the class closest to matrices with commutative elements. Determinants...