Contraction criteria for reducible rational curves with components of length one in smooth complex threefolds
نویسندگان
چکیده
منابع مشابه
Contraction Criteria for Reducible Rational Curves with Components of Length One in Smooth Complex Threefolds
Let X be a smooth complex threefold and C a linear chain of n smooth rational curves in X, each intersecting the canonical sheaf KX trivially, and each having length 1, where the length is Kollár’s invariant. Formal criteria will be given to determine when C contracts, when C deforms, and when C neither contracts or deforms in X̂, the formal completion of X. It is shown precisely, using the curv...
متن کاملVersal deformations and superpotentials for rational curves in smooth threefolds
My interests in the study of curves on Calabi-Yau threefolds have largely been shaped in two ways: by the tutelage and guidance of Herb Clemens while I was an instructor at the University of Utah in the early 80’s, and by the interaction between geometry and string theory. This note is the result of both of these influences. Herb impressed upon me the importance of the consideration of elementa...
متن کاملRational Curves on Fano Threefolds of Picard Number One
Rational Curves on Fano Threefolds of Picard Number One
متن کاملRational Curves on Calabi-yau Threefolds
In the conformal field theory arising from the compactification of strings on a Calabi-Yau threefold X, there naturally arise fields correspond to harmonic forms of types (2,1) and (1,1) on X [4]. The uncorrected Yukawa couplings in H and H are cubic forms that can be constructed by techniques of algebraic geometry — [20] contains a nice survey of this in a general context in a language written...
متن کاملSmooth rationally connected threefolds contain all smooth curves
It is very easy to see that every smooth projective curve can be embedded in P3. Eisenbud and Harris asked whether the same is true if P3 is replaced by an arbitrary smooth rational projective 3-fold X and Eisenbud suggested starting with the case where X is toric. In that case the answer is yes, and one can see that in a very explicit way, as was done in my preprint [Sa2]. In response to [Sa2]...
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: Pacific Journal of Mathematics
سال: 2003
ISSN: 0030-8730
DOI: 10.2140/pjm.2003.212.377