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**Staff.ustc.edu.cn** **DA:** 17 **PA:** 48 **MOZ Rank:** 65

**codimX**1 \X 2 =**codimX**1 +**codimX**2: Finally we prove the following transversality theorem which is useful in nding transversal maps:(In general Mcould be a manifold with boundary, but we will not discuss that here.) Theorem 2.7 (The Transversality Theorem)- Let F: S M!Nbe a smooth map, XˆNbe a smooth submanifold

**Math.mit.edu** **DA:** 12 **PA:** 33 **MOZ Rank:** 46

- Standard specialization argument for reducing to the case F = F q: 1
- X ˆPn F is the base change of some X ˆPn R, for some nitely generated Z-subalgebra R ˆF, such that X !SpecR has geometrically irreducible bers all of the same dimension
- 2.There is a big bad M bad ˆP n R such that for any R- eld k, the ber (M bad) k is the

**Metaphor.ethz.ch** **DA:** 16 **PA:** 37 **MOZ Rank:** 55

- codimV(a) = heighta;
**codimX**= heightI(X) for any ideal a and any closed X Spec(A) - Lemma 1 says that dimX+
**codimX**dimSpecA - 4 Primeavoidancelemma Lemma 5.LetAbearing,letp 1;:::;p n beprimeideals,andleta beanideal contained in the union [p j
- Then there exists an index j for which a p j
- Equivalently,ifa 6 p j foreachj,thena 6 [p j

**Math.purdue.edu** **DA:** 19 **PA:** 23 **MOZ Rank:** 45

- the convention that
**codimx**= n + 1 iﬀ x = ∅ - We use (3) to extend the deﬁnition of admissibility to systems of arbitrary cardinality
- So a system of hyperplanes will be called admissible if any k ≤ n + 1 vectors α deﬁning these hyperplanes as in (1) are linearly independent.

**Sciencedirect.com** **DA:** 21 **PA:** 38 **MOZ Rank:** 63

- Then, the degree and the codimension of X satisfy the inequality degX greaterorequalslant
**codimX**+ 1 (cf - Varieties for which equality holds are called varieties of minimal degree
- These varieties are completely classified (cf
- In particular they are arithmetically Cohen–Macaulay and have a linear

**Users.math.yale.edu** **DA:** 19 **PA:** 50 **MOZ Rank:** 74

- ducible manifold X~_CP '~, tangent to
**codimX**generic submanifolds is admissible - Then X is a manifold of minimal degree
- Differential-Geometric Applications
- Let {B$} be a 2-parameter family of curves on the surface B, $~F
- Then a generic point x~B defines a curve F x on the surface of

**Publications.ias.edu** **DA:** 20 **PA:** 35 **MOZ Rank:** 61

**codimx**(Z~) = eodiml~x~ (Z) at all points x EA- There are two basic questions with which we shall deal: (A) Can we find an upper bound on the size of Z I in terms of Z and the "growth" of the mapping ]? NEVANLINNA THEORY AND HOLOMORPHIC MAPPINGS BETWEEN ALGEBRAIC VARIETIES 147 (B) Can we find a lower bound on

**Math.uni-sb.de** **DA:** 18 **PA:** 50 **MOZ Rank:** 75

- vanishes at z = 1 to the order c =
**codimX** - Let F= Me be the associated coherent sheaf on Pn of a graded module M
- Then: pM(k) = χ(F(k)) = P n i=0 (−1) ihi(F(k)) for all k
- A family of sheaves F τ is ﬂat, iff the coefﬁcients of the Hilbert polynomials are constant as functions of τ.

**Math.ualberta.ca** **DA:** 20 **PA:** 41 **MOZ Rank:** 69

- If the homogeneous equation (3) is asymptotically stable and, for some f(t), there is a solution x0(t) of the nonhomogeneous equation (1) such that limt!1 x0(t) = 0, then all solutions of the equa- tion (1) satisfy limt!1 x(t) = 0
- This follows from the fact that for

**People.math.wisc.edu** **DA:** 20 **PA:** 33 **MOZ Rank:** 62

- assumed to be over a eld k of characteristic zero or greater than
**codimX** - This paper grew out of conversations with Tony Pantev, Lev Rozansky, and Craig Westerland
- The rst author is a Sloan Research Fellow and he is grateful to the Alfred P
- Sloan Foundation for the support.

**Gdenham.math.uwo.ca** **DA:** 19 **PA:** 26 **MOZ Rank:** 55

**codimX**: If K = C, then ˇ(A;t) = Poin(Cℓ n[H2AH;t): It is known that ˇ(A;t) is combinatorial (i.e., determined by L(A))- Hence so are all Betti numbers of the complemeht M(A) …

**Www2.math.upenn.edu** **DA:** 19 **PA:** 42 **MOZ Rank:** 72

- dimX= 1 or
**codimX**= 1, as we will explain in (2.5.1(b)), the computation is trivial simply because the closed ﬁber X k “does not have many subgroups” - In this section, we will compute a ﬁrst non-trivial example

**Uta.edu** **DA:** 11 **PA:** 40 **MOZ Rank:** 63

- By the theoretical equivalence of (3) to the standard Hermitian eigenvalue problem (4) or (5), we know that (3) has n real eigenvalues and B-orthonormal eigenvectors
- Throughout the rest of this section, A−λB will be assumed a Hermitian matrix pencil of order n with B ≻ 0, and its eigenvalues, eigenvectors, and eigen-decomposition are given by (6).

**Math.utah.edu** **DA:** 17 **PA:** 30 **MOZ Rank:** 60

- This shows that (5) implies (6)
- Throughout, P (E) denote the conditional probability measure (expectation) P (E), given the entire process S
- With the above notation in mind, it should be recognized that, under the measure P, the process W is a centered Gaussian process with covariance

**Facebook.com** **DA:** 16 **PA:** 8 **MOZ Rank:** 38

- Somos una organización comprometida con la humanidad
- Buscamos la revolución mediante la evolución de las conciencias.

**Sciencedirect.com** **DA:** 21 **PA:** 38 **MOZ Rank:** 74

Over a Noetherian, local ring R of prime characteristic p, the Frobenius functor FR induces a diagonalizable map on certain quotients of rational Grot…

**Ams.org** **DA:** 11 **PA:** 50 **MOZ Rank:** 77

- lary 2.6], 77'(Lx, 3X) ^ 0 for some positive i <
**codimX**- 1 - Thus the same is true for H'(LX, 3) which concludes the proof
- Now let D(0) be the ¿-module of derivations corresponding to the empty arrangement in V
- Clearly it is a free module of rank /

**Math.wustl.edu** **DA:** 18 **PA:** 21 **MOZ Rank:** 56

- of the form degX
**codimX**+constant - Using projection methods of [23] and [21], Conjecture 1.3 would imply that for any smooth non-degenerate projective variety of dimension nin Pr, reg(X) deg(X) codim(X) + 1 + c n;r where c n;r= P n+1 i=3 (i 2) r n 2+i: Secant Lines …

**Www3.nd.edu** **DA:** 11 **PA:** 28 **MOZ Rank:** 57

- THE NORMAL CYCLE AND CURVATURE MEASURES 3 1
- The (co)-normal bundle of submanifolds 1.1
- Let Vbe a nite dimensional Euclidean space.

**Citeseerx.ist.psu.edu** **DA:** 21 **PA:** 16 **MOZ Rank:** 56

- CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): that maps birationally onto D and for which one can compute its class [Z]
- Usually this is because [Z] is the zero locus of a section of some bundle whose rank is equal to
**codimX**0 Z so the class [Z] is evaluated to be the top Chern class of the bundle - For example, this pattern was used in [J-L-P] and many other

**Zora.uzh.ch** **DA:** 15 **PA:** 32 **MOZ Rank:** 67

**codimX**≤ 4 by listing the possible Betti diagrams- Let us recall that the structure of arithmetically Cohen-Macaulay resp
- Gorenstein varieties in codimension 2 resp
- 3 is known by the Theorems of Hilbert-Burch resp
- So, we need not to discuss these cases in detail any more
- As the Betti diagrams, the degree and

**Jstor.org** **DA:** 13 **PA:** 23 **MOZ Rank:** 57

- (i) Suppose f is a finite morphism and
**codimx**= codimy = 1 - Then r(xy) = e(xy) - 1 if and only if the residue field k(x) of x is a separable extension of the residue field k(y) of y and e(xy) is not a multiple of the characteristic of k(y)
- (ii) Suppose f is a birational morphism

**Math.purdue.edu** **DA:** 19 **PA:** 32 **MOZ Rank:** 73

- H~(Ei, Q) =0 .for l~q~.p--
**codimX**~ - Let us assume now that all simplices X i of the combinatorial manifold X are cooriented
- For each simplex Xj we set ~(~) = {i: Xi~X], dim Xi =dim Xlq-|)
- If g~s(]), then by eij is denoted the incidence coefficient e(X i, Xj).$

**Citeseerx.ist.psu.edu** **DA:** 21 **PA:** 16 **MOZ Rank:** 60

- CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): ABSTRACT
- The present research grew out of the authors ’ joint work [2]
- It continues the study of the structure of projective varieties of almost minimal degree, focussing to the case of small codimension
- In particular, we give a complete list of all occuring Betti diagrams in the cases where
**codimX**≤ 4.

**Math.ucsd.edu** **DA:** 17 **PA:** 40 **MOZ Rank:** 81

- (b) X w= frkA rkwg=B + (compare ranks pointwise) (c) X w= ‘ rk v rkw X forms an a ne strati cation of Fl(Cn) (d) X w is an integral, Cohen-Macaulay variety
- Warning: there are (a dihedral group of order) 8 \natural" ways to reindex the X w, so there are many con icting conventions and de nitions in the

**Semanticscholar.org** **DA:** 23 **PA:** 50 **MOZ Rank:** 98

- The tangential branch locus B X/Y ⊂ BX/Y is the subset of points in the branch locus where the sheaf of relative vector fields TX/Y fails to be locally free
- It was conjectured by Zariski and Lipman that if V/k is a variety over a field k of characteristic 0 and B V/k = ∅, then V/k is smooth (=regular)
- We prove this conjecture when V/k is a locally complete intersection.

**People.math.osu.edu** **DA:** 19 **PA:** 38 **MOZ Rank:** 83

- EQUIVARIANT COHOMOLOGY IN ALGEBRAIC GEOMETRY 5 Let DJ: H∗ TX→ H∗ TXbe the Λ-linear map deﬁned by DJ = (πJ) ∗ (πJ)∗
- This lowers degree by twice the codimension, i.e., by 2#(R+ J)
- (1) If w− is the minimal representative of its coset in W/WP, then DJ(x(w−)) = x(w+), where w+ is the maximal representative of the coset

**Math.fsu.edu** **DA:** 16 **PA:** 29 **MOZ Rank:** 72

- GROTHENDIECK CLASSES AND CHERN CLASSES OF HYPERPLANE ARRANGEMENTS 5 2.2
- Our rst task is the computation of the Grothendieck class of the complement

**Upcommons.upc.edu** **DA:** 17 **PA:** 18 **MOZ Rank:** 63

- For any finite abelian group G , we provide an explicit construction of
**codimX**polynomial equations (phylogenetic invariants) of degree at most |G| that define the variety X on a Zariski open set U - The set U contains all biologically meaningful points when G is the group of the Kimura 3-parameter model.

**Www3.nd.edu** **DA:** 11 **PA:** 29 **MOZ Rank:** 69

- The set W= X\Lis called a witness point set for X
- 3 Method For a pure-dimensional generically reduced scheme XˆPn, one can determine that Xis arith-metically Gorenstein by combining Theorems 1 and 2
- We describe the zero-dimensional and positive-dimensional cases below
- A generalization of this approach, using Macaulay dual

**Web.williams.edu** **DA:** 16 **PA:** 50 **MOZ Rank:** 96

- NOTES ON TALKS AT THE SIMONS SYMPOSIUM ON FAMILIES OF AUTOMORPHIC FORMS AND THE TRACE FORMULA STEVEN J
- MILLER ABSTRACT.The following are notes on the talks at the Simons Symposium on Families of Automorphic Forms

**Jstor.org** **DA:** 13 **PA:** 23 **MOZ Rank:** 67

- where Z runs over closed irreducible subschemes with
**codimx**Z > r, and W runs over nonsingular complex projective varieties of dimension dim X - q with a morphism W -? X (inducing a Gysin map on cohomology), for q > r, and U runs over Zariski-open subsets of X with codim(X - U) > r

**Web.ma.utexas.edu** **DA:** 17 **PA:** 50 **MOZ Rank:** 99

- Lifting
**Tropical Intersections**123 say that Trop(X) meets Trop(X′) properly if they meet properly at every point of their intersection, which may be empty.1 Theorem 1.1 - Suppose Trop(X) meets Trop(X′) properly at w.Then w is contained in the tropicalization of X ∩X′
- In other words, tropicalization commutes with intersections when the inter-

**Books.google.com** **DA:** 16 **PA:** 50 **MOZ Rank:** 99

- Algebraic Cycles and Motives: Volume 2
- Johannes Nagel, Jan Nagel, Chris Peters
- Cambridge University Press, May 3, 2007 - Mathematics - 359 pages
- Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme
- Alexander Grothendieck taught that algebraic cycles should be considered from a

**Pi.math.cornell.edu** **DA:** 19 **PA:** 28 **MOZ Rank:** 81

- 2 ALLEN KNUTSON (Warning: being “open strata” doesn’t mean they’re open in X– we’ll reserve the term maximal open strata for this.) In particular Y is a poset, deﬁning1 Z ≤ Y for Z ⊆ Y
- One of the obvious sources of such decompositions is the orbits of a group action.

**Rangevoting.org** **DA:** 15 **PA:** 21 **MOZ Rank:** 71

- • L has a rank function given by r(X) =
**codimX** - Thus r(V) = 0 and r(H) = 1 for H ∈ A
- • The join X ∨Y is given by X ∩Y, if it is nonempty
- • The meet X ∧Y is given by T {Z | Z ∈ L, X ∪Y ⊂ Z}
- We say that an element X covers an element Y if X has rank 1 greater than

**Upcommons.upc.edu** **DA:** 17 **PA:** 48 **MOZ Rank:** 14

Scheme of pairs of matrices with vanishing commutator Bartomeu Llopis Vidal May 2019 ThesissubmittedinpartialfulﬁlmentoftherequirementsfortheBachelor’s

**Deepblue.lib.umich.edu** **DA:** 22 **PA:** 50 **MOZ Rank:** 13

- that Proposition 2.1 can be improved to the statement that
**codimX**i 3(‘−i) for 0 i ‘−1 - Panyushev informs us that he has been able to prove this by acasebycaseanalysis
- Fix a G-invariant, non-degenerate, symmetric bilinear form on g and let ~ : g!g be the induced isomorphism
- Thus, ~ induces an isomorphism between

**Depts.washington.edu** **DA:** 20 **PA:** 26 **MOZ Rank:** 84

Riemann–HilbertProblems,TheirNumericalSolutionandthe ComputationofNonlinearSpecialFunctions Thomas D. Trogdon A dissertation submitted in partial fulﬁllment of the

**Storage.googleapis.com** **DA:** 22 **PA:** 50 **MOZ Rank:** 11

- α) are closed, codimYα = codimXα = k, the maps Fα k: X α → Yα are onetoone and the maps ( Fα k) −1 are locally uniformly continuous for all k large enough
- Quasiruled maps appear in the following situation
- Suppose X˜, Y˜ are Banach spaces, X ⊂ X˜, Y ⊂ Y˜, and the …

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