TANGENTS AND SECANTS OF ALGEBRAIC VARIETIES F. L. Zak

... From this it follows that either all n-dimensional linear subspaces from γn (X) are contained in an (n + 1)-dimensional linear subspace Pn+1 ⊂ PN or they all pass through an (n − 1)-dimensional subspace Pn−1 ⊂ PN . But in the first case X is a hypersurface and by Theorem 1.7 dim Yα = n − 1 ≤ b + 1, ...

... From this it follows that either all n-dimensional linear subspaces from γn (X) are contained in an (n + 1)-dimensional linear subspace Pn+1 ⊂ PN or they all pass through an (n − 1)-dimensional subspace Pn−1 ⊂ PN . But in the first case X is a hypersurface and by Theorem 1.7 dim Yα = n − 1 ≤ b + 1, ...

Archimedean Rankin Selberg Integrals

... (n, n) the relevant L-factor is obtained in terms of vectors which are finite under the appropriate maximal compact subgroups. The result is especially simple in the unramified situation, a result proved by Stade ([22], [23]) with a different proof. A first version of these notes was published earli ...

... (n, n) the relevant L-factor is obtained in terms of vectors which are finite under the appropriate maximal compact subgroups. The result is especially simple in the unramified situation, a result proved by Stade ([22], [23]) with a different proof. A first version of these notes was published earli ...

COMMUTATIVE ALGEBRA Contents Introduction 5

... I. Commutative algebra is a necessary and/or useful prerequisite for the study of other ﬁelds of mathematics in which we are interested. II. We ﬁnd commutative algebra to be intrinsically interesting and we want to learn more. Perhaps we even wish to discover new results in this area. Most beginning ...

... I. Commutative algebra is a necessary and/or useful prerequisite for the study of other ﬁelds of mathematics in which we are interested. II. We ﬁnd commutative algebra to be intrinsically interesting and we want to learn more. Perhaps we even wish to discover new results in this area. Most beginning ...

higher algebra

... 9.2.2 Special features of localization in domains. . . . . . . . 295 9.2.3 Localization at a prime ideal. . . . . . . . . . . . . . . 296 9.3 Unique Factorization. . . . . . . . . . . . . . . . . . . . . . . . 297 9.3.1 A Special Case. . . . . . . . . . . . . . . . . . . . . . . 301 9.4 Euclidean Do ...

... 9.2.2 Special features of localization in domains. . . . . . . . 295 9.2.3 Localization at a prime ideal. . . . . . . . . . . . . . . 296 9.3 Unique Factorization. . . . . . . . . . . . . . . . . . . . . . . . 297 9.3.1 A Special Case. . . . . . . . . . . . . . . . . . . . . . . 301 9.4 Euclidean Do ...