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Effective Hilbert irreducibility

Erich Kaltofen
1985 Information and Control  
n this paper we prove by entirely elementary means a very effective version of the Hilbert Irreducibility n Theorem.  ...  Hilbert Irreducibility Theorem, Probabilistic Algorithms, Polynomial Factorization, Sparse Polynomials.  ...  We now formulate our irreducibility theorem in the most general way we shall prove T here. heorem 3 (Effective Hilbert Irreducibility Theorem): Let f (x ,..., x ) ∈ F [x ,..., x ], F a 1 v 1 v h c field  ... 
doi:10.1016/s0019-9958(85)80056-5 fatcat:6ir4lipfrjb4poge545eeuzeim

Effective Hilbert irreducibility [chapter]

Erich Kaltofen
EUROSAM 84  
n this paper we prove by entirely elementary means a very effective version of the Hilbert Irreducibility n Theorem.  ...  Hilbert Irreducibility Theorem, Probabilistic Algorithms, Polynomial Factorization, Sparse Polynomials.  ...  We now formulate our irreducibility theorem in the most general way we shall prove T here. heorem 3 (Effective Hilbert Irreducibility Theorem): Let f (x ,..., x ) ∈ F [x ,..., x ], F a 1 v 1 v h c field  ... 
doi:10.1007/bfb0032850 dblp:conf/eurosam/Kaltofen84 fatcat:siyfi43dzrfwhc36n2j6b5cema

Page 7693 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Sci. 72 (1996), no. 7, 135-138; MR 97k:14003] to the effect that the crepant resolution of C”/G for a finite subgroup G C SL,(C) could be closely related to the G-Hilbert scheme Hilb°(C”") of G-stable  ...  In particular, since standard determinantal schemes are aCM, The- orem 2.8 supplies a class of Hilbert functions of irreducible and reduced aCM schemes.  ... 

Multipartite Quantum Systems and Representations of Wreath Products

Vladimir Kornyak, Gh. Adam, J. Buša, M. Hnatič
2020 EPJ Web of Conferences  
The program, in particular, builds irreducible invariant projectors in the Hilbert space of a multipartite system. The expressions for these projectors are tensor product polynomials.  ...  We describe an algorithm for decomposing representations of wreath products into irreducible components.  ...  The computer implementation of the algorithm in [6] proved to be very effective in problems with low ranks.  ... 
doi:10.1051/epjconf/202022602013 fatcat:5u4nfvli45frpcz4z5ysix2yfy

Page 174 of Mathematical Reviews Vol. 33, Issue 1 [page]

1967 Mathematical Reviews  
U™ of U is irreducible if U is; a converse is stated, to the effect that if U is either inequivalent to its complex conjugate, or “real”, and irreducible, then U is irre- ducible.  ...  Irreducibility is then defined, as well as reducibility, which is connected with superselection rules.  ... 

On a conjecture due to Griffiths and Harris [article]

Ananyo Dan
2014 arXiv   pre-print
It is known (due to works of Voisin, Green and others) that the largest irreducible component is of codimension (in the space of all smooth surface in P^3 of degree d) equal to d-3.  ...  Furthermore, the irreducible component of this locus parametrizing surfaces with r lines on the same plane is of this codimension. In this article we prove the statement for d ≫ r.  ...  Then, [Blo72, Theorem 7.1] implies that the class of [C i ] remains effective along NL(Λ ′ ). This proves the proposition.  ... 
arXiv:1404.5717v2 fatcat:hrwycsxk7bdlzc7krmx2a3nefa

Noether-Lefschetz locus and generalisation of an example due to Mumford [article]

Ananyo Dan
2014 arXiv   pre-print
In this article we generalise the well-known example due to Mumford for a generically non-reduced component of the Hilbert scheme of curves in P^3 whose general element is smooth.  ...  In this article we give similar examples of generically non-reduced component of the Hilbert scheme of curves in P^3, for every integer d > 5, whose general element is a smooth curve contained in a smooth  ...  In particular, if we denote by P the Hilbert polynomial of this curve, there exists an irreducible component H γ of the flag Hilbert scheme Hilb P,Q d such that pr 2 (H γ ) red ∼ = NL(γ) red and H  ... 
arXiv:1409.6012v1 fatcat:okjz4ozdzjd77lclfnvcpptvtu

On Serre's uniformity conjecture for semistable elliptic curves over totally real fields

Samuele Anni, Samir Siksek
2015 Mathematische Zeitschrift  
We combine this with modularity and level lowering to show the existence of an effectively computable constant C_K,S, and an effectively computable set of elliptic curves over K with CM E_1"E_n such that  ...  follows from the work of Merel, Momose and David that there is a constant B_K,S so that if E is an elliptic curve defined over K, semistable outside S, then for all p>B_K,S, the representation ρ̅_E,p is irreducible  ...  So far we proved that there are an effectively computable constant C K,S and a finite computable set f 1 , . . . , f n of Hilbert eigenforms over K of parallel weight 2 with Q-rational eigenvalues such  ... 
doi:10.1007/s00209-015-1478-8 fatcat:wmkruxhtcrefbnqhx6c6clplee

Page 8719 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
For topological algebras, the concrete models we use are effective representation by algebraic domains (Stoltenberg-Hansen and Tucker), effective representa- tion by continuous domains (Edelat) and effective  ...  T is said to be strongly irreducible if T does not commute with any nontrivial idempotent; the collection of strongly irreducible opera- tors is designated by (SI).  ... 

Hilbert irreducibility sequences and nonstandard arithmetic

M. Yasumoto
1987 Journal of Number Theory  
We give sufticient conditions for a sequence of integers to be a Hilbert irreducibility sequence and give such a sequence explicitly.  ...  2"2 ' IS a Hilbert irreducibility sequence. Moreover he proved that there is an effectively computable function n,(f) such that f(X, a,) is irreducible for all n >rt,(f). (See also 121).  ...  A sequence is called a Hilbert irreducibility sequence (H.i.seq.) if it is an m-irreducibility sequence for all natural numbers m.  ... 
doi:10.1016/0022-314x(87)90084-9 fatcat:g7us5jfez5aeli34yykuqtx4ee

A Poincaré invariant treatment of the three-nucleon problem [article]

W. Polyzou, M. Tucker, S. Veerasamy, Ch. Elster, T. Lin, W. Glöckle, H. Witała, J. Golak, R. Skibiński, H. Kamada, B. Keister
2008 arXiv   pre-print
We denote the single nucleon Hilbert space by H 1 . There is a natural unitary irreducible representation of the Poincaré group on H 1 .  ...  The Hilbert space in these models is the tensor product of mass m spin 1/2 irreducible representation spaces of the Poincaré group, where m is the nucleon mass.  ... 
arXiv:0812.2204v1 fatcat:22rmxxafz5fxzegure44y7k4hu

Kirillov's character formula, the holomorphic Peter–Weyl theorem, and the Blattner–Kostant–Sternberg pairing

Johannes Huebschmann
2008 Journal of Geometry and Physics  
of the irreducible representations of K by the appropriate operation of Hilbert space sum.  ...  We establish the statement of the Peter-Weyl theorem for this Hilbert space to the effect that this Hilbert space contains the vector space of representative functions on G as a dense subspace and that  ...  K abelian: measure on K C Haar measure on K times Gaussian in imaginary directions decomposition of the Hilbert spaces into irreducible (1-dimensional) constituents: inspection of characters establishes  ... 
doi:10.1016/j.geomphys.2008.02.004 fatcat:yp3itk6lzbhtbhj3txjq5ebg4u

Bounds on the Torsion Subgroups of Néron-Severi Groups [article]

Hyuk Jun Kweon
2019 arXiv   pre-print
The bounds are derived from an explicit upper bound on the number of irreducible components of either the Hilbert scheme Hilb_Q X or the scheme CDiv_n Xparametrizing the effective Cartier divisors of degree  ...  Given a graded module M over k, let HP M be the Hilbert polynomial of M , and M t be the degree t part of M . Take an effective divisor D on X.  ...  Once a Hilbert scheme is explicitly constructed, we can bound the number of the irreducible components by the lemma below. Lemma 4.6.  ... 
arXiv:1902.02753v2 fatcat:v6ioixaegbbfjgjzhxexxsokyq

On the Hilbert scheme of curves in higher-dimensional projective space [article]

Barbara Fantechi, Rita Pardini
1995 arXiv   pre-print
In this paper we prove that, for any n> 3, there exist infinitely many r∈ and for each of them a smooth, connected curve C_r in ^r such that C_r lies on exactly n irreducible components of the Hilbert  ...  of the Hilbert scheme.  ...  Then there exist infinitely many integers r, and for each of them a smooth, irreducible curve C r ⊂ IP r such that C r lies exactly on n components of the Hilbert scheme of IP r .  ... 
arXiv:alg-geom/9501009v1 fatcat:gwzj6dmk6jdvnowoavgp2jdqna

Hilbert property for double conic bundles and del Pezzo varieties [article]

Sam Streeter
2020 arXiv   pre-print
We then give an application of this result, namely the verification of the Hilbert property for certain del Pezzo varieties.  ...  In this paper we prove that, over a Hilbertian ground field, surfaces with two conic fibrations whose fibres have non-zero intersection product have the Hilbert property.  ...  Then C × P 1 D is a regular, geometrically irreducible curve. Proof.  ... 
arXiv:1812.05937v5 fatcat:2dkz3f35vrdfbctf7ddb5qswwa
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