Polynomial mappings with small degree

• Autorzy: Jelonek Z.
• Języki publikacji: EN

Abstrakty

EN

Let Xn be an affine variety of dimension n and Yn be a quasi-projective variety of the same dimension. We prove that for a quasi-finite polynomial mapping f : Xn → Yn ,every non-empty component of the set Yn\f(Xn) is closed and it has dimension greater or equal to (…), where (…) is a geometric degree of f. Moreover, we prove that generally, if (…) is any polynomial mapping, then either every non-empty component of the set (…) is of dimension (…) or f contracts a subvariety of dimension (…).

Słowa kluczowe

EN

affine space; set of non proper points; polynomial mapping

PL

przestrzeń afiniczna; odwzorowanie wielomianowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 2
• Strony: 242--249
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Jelonek Z.

• Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-656 Warszawa, Poland

Bibliografia

• [1] A. Grothendieck, Etude locale des schemas et des morphismes de schemas (EGA 4), Publ. Math. IHES 28 (1966).
• [2] R. Hartshorne, Algebraic Geometry, Springer, New York, 1987.
• [3] S. Iitaka, Algebraic Geometry, Springer, 1982.
• [4] Z. Jelonek, Testing sets for properness of polynomial mappings, Math. Ann. 315 (1999), 1–35.
• [5] Z. Jelonek, A complement of a hypersurface in affine variety, Bull. Acad. Polon. Sci. Math. 49 (2001), 375–379.
• [6] Z. Jelonek, Topological characterization of finite mappings , Bull. Acad. Polon. Sci. Math. 49 (2001), 279–283.
• [7] I. R. Shafarevich, Basic Algebraic Geometry, Springer, 1974.