منابع مشابه
Projective Product Spaces
Let n = (n1, . . . , nr). The quotient space Pn := Sn1× · · ·×Snr/(x ∼ −x) is what we call a projective product space. We determine the integral cohomology ring H∗(Pn) and the action of the Steenrod algebra on H∗(Pn;Z2). We give a splitting of ΣPn in terms of stunted real projective spaces, and determine when Si is a product factor of Pn. We relate the immersion dimension and span of Pn to the ...
متن کاملVirtual Resolutions for a Product of Projective Spaces
Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are too long and contain many geometrically superfluous summands. In this paper, we construct some much shorter free complexes that better encode the ge...
متن کاملProjective embedding of projective spaces
In this paper, embeddings φ : M → P from a linear space (M,M) in a projective space (P,L) are studied. We give examples for dimM > dimP and show under which conditions equality holds. More precisely, we introduce properties (G) (for a line L ∈ L and for a plane E ⊂ M it holds that |L ∩ φ(M)| 6 = 1) and (E) (φ(E) = φ(E) ∩ φ(M), whereby φ(E) denotes the by φ(E) generated subspace of P ). If (G) a...
متن کاملCup product and intersection
This is a handout for my algebraic topology course. The goal is to explain a geometric interpretation of the cup product. Namely, if X is a closed oriented smooth manifold, if A and B are oriented submanifolds of X, and if A and B intersect transversely, then the Poincaré dual of A∩B is the cup product of the Poincaré duals of A and B. As an application, we prove the Lefschetz fixed point formu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1970-0259947-2