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2 Preface In response to the growing interest in building a Neutrino F actory to produce high intensity beams of electron-and muon-neutrinos and antineutrinos, in October 1999 the Fermilab Directorate initiated two six-month studies. The first study, organized by N. Holtkamp and D. Finley, was to investigate the technical feasibility of an intense neutrino(More)
The Hilbert scheme H d n of n points in A d contains an irreducible component R d n which generically represents n distinct points in A d. We show that when n is at most 8, the Hilbert scheme H d n is reducible if and only if n = 8 and d ≥ 4. In the simplest case of reducibility, the component R 4 8 ⊂ H 4 8 is defined by a single explicit equation which(More)
Let X be a del Pezzo surface of degree one over an algebraically closed field, and let Cox(X) be its total coordinate ring. We prove the missing case of a conjecture of Batyrev and Popov, which states that Cox(X) is a qua-dratic algebra. We use a complex of vector spaces whose homology determines part of the structure of the minimal free Pic(X)-graded(More)
We prove that the determinantal complexity of a hypersurface of degree d > 2 is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5. As a result, we obtain that the determinantal complexity of the 3 × 3 permanent is 7. We also prove that for n > 3, there is no nonsingular hypersurface in P n of(More)