Related papers: A local version of the Fulton-Hansen theorem relat…
This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.
We study the local differential geometry of varieties $X^n\subset \Bbb C\Bbb P^{n+a}$ with degenerate secant and tangential varieties. We show that the second fundamental form of a smooth variety with degenerate tangential variety is…
This paper has been withdrawn by the author due to a crucial error.
This paper has been withdrawn due to a crucial theoretical error.
This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.
We correct a mistake in an earlier paper and give a complete classification of singular varieties having an extremal secant line.
This paper has been withdrawn by the authors due to an error.
This paper has been withdrawn due to a crucial theoretical and experimental error.
This paper has been withdrawn. Theorem 2.1 of the paper is false, as it contradicts a result of Srinvas (Crelle's J. v.381, 1987). The error in our proof is in the construction of a functor in Claim 2. What we construct does not preserve…
The main goal of this paper is to study some local and global properties of secant varieties of algebraic curves. These results complement our previous work [8] by addressing issues given therein and providing solutions to problems raised…
The paper has been withdrawn by the author, due to a critical error stemming from the defined template.
This paper has been withdrawn by the author due to a crucial error in example.
We give an exposition of the formal aspects of deformation theory in the language of fibered categories, instead of the more traditional one of functors. The main concepts are that of tangent space to a deformation problem, obstruction…
These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field…
This paper has been withdrawn by the authors. Some of the arguments developed in the paper are erroneous. They will be rectified in a later publication.
This paper has been withdrawn due to an incorrect analysis in Section 4.
The paper submitted has been withdrawn for revision. Example 1 is incorrect; the map is not a local homeomorphism.
In this paper, we develop a theory of pseudo-effective sheaves on normal projective varieties. As an application, by running the minimal model program, we show that projective klt varieties with pseudo-effective tangent sheaf can be…
This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial