A vector bundle characterization of pn (original) (raw)

Abstract

The following is a natural conjecture.

FAQs

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What explains the correlation between E's spanned sections and X's structure?add

The paper demonstrates that if E is spanned and c_n(E) = 1, X must be rational, implying a relationship with projective spaces.

When did the authors establish the conjecture for n = 2 and n = 3?add

They proved the conjecture for n = 2 and n = 3 with isolated singularities, contributing significantly to understanding vector bundles on projective varieties.

How does the paper build on previous research by WlSNmWSKI?add

The findings leverage Mori theory results established in WlSNmWSKI's Notre Dame thesis to support their conjecture for smooth varieties.

What results were derived regarding hyperplane sections of threefolds?add

The corollary indicates that for n = 2, the conjecture provides insights on nontrivial hyperplane sections, enhancing the study of threefolds.

Why is the condition of Gorenstein crucial for the results?add

The Gorenstein condition is critical as it ensures isolated singularities, which are essential for the structure of X when n = 3.

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References (9)

  1. W. FULTON, Intersection Theory, Springer Verlag, Berlin, 1984.
  2. A. LANTERI and D. STRUPPA, Projective manifolds whose topology is strongly reflected in their hyperplane sections, Geometriae Dedicata 21 (1986), 357-374.
  3. R. LAZARSFELD, Some applications of the theory of positive vector bundles, Complete Intersections, Proc. Acireale, 1983, Springer Lecture Notes 1092 (1984), 29-61.
  4. C. OKONEK, M. SCHNEIDER, H. SPINDLER, Vector Bundles on Complex Projecti- ve Spaces, Progress in Math. 3, Birkh/iuser, Boston, 1980.
  5. A. J. SOMMESE, On the adjunction theoretic structure of projective varieties, Proc. Complex Analysis and Algebraic Geometry Conference, ed. by H. Grauert, G6ttingen, 1985, Springer Lecture Notes 1194 (1986), 175-213.
  6. A. J. SOUMESE and A. VA~ DE VEN, On the adjunction mapping, preprint.
  7. J. WISNIEWSKI, Length of extremal rays and a characterization of projective space, preprint. Eingegangen am 21.01.1987
  8. Anschrift der Autoren: Antonio Lanteri, Dipartimento di Matematica ,F. Enriques~, dell'UniversitY, Via C. Saldini, 50, 1-20133 Milano, Italia;
  9. Andrew J. Sommese, Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.