scholarly journals Lefschetz type formulas for dg-categories

2013 ◽  
Vol 20 (3) ◽  
pp. 885-928 ◽  
Author(s):  
Alexander Polishchuk
Keyword(s):  
Lefschetz Type

scholarly journals A BARTH–LEFSCHETZ THEOREM FOR SUBMANIFOLDS OF A PRODUCT OF PROJECTIVE SPACES

2009 ◽  
Vol 20 (01) ◽  
pp. 77-96
Author(s):  
LUCIAN BĂDESCU ◽  
FLAVIA REPETTO
Keyword(s):  
Normal Bundle ◽  
Projective Spaces ◽  
Restriction Map ◽  
Vanishing Theorem ◽  
Type Result ◽  
Picard Groups ◽  
Lefschetz Type ◽  
Simply Connected ◽  
Join Construction ◽  
Torsion Free

Let X be a complex submanifold of dimension d of ℙm × ℙn (m ≥ n ≥ 2) and denote by α: Pic(ℙm × ℙn) → Pic(X) the restriction map of Picard groups, by NX|ℙm × ℙn the normal bundle of X in ℙm × ℙn. Set t := max{dim π1(X), dim π2(X)}, where π1 and π2 are the two projections of ℙm × ℙn. We prove a Barth–Lefschetz type result as follows: Theorem. If [Formula: see text] then X is algebraically simply connected, the map α is injective and Coker(α) is torsion-free. Moreover α is an isomorphism if [Formula: see text], or if [Formula: see text] and NX|ℙm×ℙn is decomposable. These bounds are optimal. The main technical ingredients in the proof are: the Kodaira–Le Potier vanishing theorem in the generalized form of Sommese ([18, 19]), the join construction and an algebraization result of Faltings concerning small codimensional subvarieties in ℙN (see [9]).

AN ${\rm SL}(2, {\mathbb C})$ ACTION ON CHIRAL RINGS AND THE MIRROR MAP

1992 ◽  
Vol 07 (35) ◽  
pp. 3277-3289 ◽  
Author(s):  
TRISTAN HÜBSCH ◽  
SHING-TUNG YAU
Keyword(s):  
Complex Structure ◽  
Inner Product ◽  
General Definition ◽  
Canonical Class ◽  
Hodge Operator ◽  
Volume Limit ◽  
Chiral Rings ◽  
Lefschetz Type ◽  
Definition Of ◽  
Mirror Map

Each transversal degree-d hypersurface ℳ in a weighted projective space defines a Landau-Ginzburg orbifold, the superpotential of which equals the defining polynomial of ℳ. For a generic such ℳ with trivial canonical class, the degree-0 (mod d) subring of the Jacobian ring (that is, the (c, c)-ring of the Landau-Ginzburg orbifold) is shown to admit an [Formula: see text] action and the corresponding Lefschetz-type decomposition. This leads to a general definition of a “large complex structure” limit, the mirror of the “large volume” limit, and the mirror images on ⊕qH3−q,q of the Hodge *-operator, duality and inner product on ⊕qHq,q.

A Lefschetz type result for Koszul cohomology

2004 ◽  
Vol 114 (4) ◽  
Author(s):  
Marian Aprodu ◽  
Jan Nagel
Keyword(s):  
Type Result ◽  
Lefschetz Type ◽  
Koszul Cohomology

scholarly journals A Lefschetz-type fixed point theorem

1975 ◽  
Vol 88 (2) ◽  
pp. 103-115 ◽  
Author(s):  
L. Górniewicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Lefschetz Type

scholarly journals Lefschetz Numbers for C*-Algebras

2011 ◽  
Vol 54 (1) ◽  
pp. 82-99 ◽  
Author(s):  
Heath Emerson
Keyword(s):  
Classical Case ◽  
Lefschetz Number ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
C Algebras ◽  
Lefschetz Numbers ◽  
The Matrix ◽  
Lefschetz Type ◽  
Polynomial Formula ◽  
Infinite Set

AbstractUsing Poincaré duality, we obtain a formula of Lefschetz type that computes the Lefschetz number of an endomorphism of a separable nuclear C*-algebra satisfying Poincaré duality and the Kunneth theorem. (The Lefschetz number of an endomorphism is the graded trace of the induced map on K-theory tensored with ℂ, as in the classical case.) We then examine endomorphisms of Cuntz–Krieger algebras OA. An endomorphism has an invariant, which is a permutation of an infinite set, and the contracting and expanding behavior of this permutation describes the Lefschetz number of the endomorphism. Using this description, we derive a closed polynomial formula for the Lefschetz number depending on the matrix A and the presentation of the endomorphism.

scholarly journals A Noether-Lefschetz theorem for varieties of r-planes in complete intersections

2012 ◽  
Vol 206 ◽  
pp. 39-66
Author(s):  
Zhi Jiang
Keyword(s):  
Type Theorem ◽  
Complete Intersections ◽  
Lefschetz Theorem ◽  
Lefschetz Type

AbstractWe prove a Noether-Lefschetz type theorem for varieties ofr-planes in complete intersections. We then use it to study the Abel-Jacobi map of planes on a smooth cubic fivefold.

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