28 citations · 79 across the 17 of their papers we have counts for
17 papers
Non-general type surfaces in P4, an update
Hirotachi Abo, Kristian Ranestad, Frank-Olaf Schreyer
A general algebraic surface cannot be embedded in P4. Proving a conjecture by Hartshorne and Lichtenbaum, Ellingsrud and Peskine showed that there is a degree bound for smooth rati…
A vector bundle approach to Nash equilibria
Hirotachi Abo, Irem Portakal, Luca Sodomaco
We use vector bundles to study the locus of totally mixed Nash equilibria of an -player game in normal form, which we call the Nash equilibrium scheme. When the payoff tensor fo…
Non-defectivity of Segre-Veronese varieties
Hirotachi Abo, Maria Chiara Brambilla, Francesco Galuppi +1
We prove that Segre-Veronese varieties are never secant defective if each degree is at least three. The proof is by induction on the number of factors, degree and dimension. As a c…
Ramification and Discriminants of Vector Bundles and a Quick Proof of Bogomolov's Theorem
Hirotachi Abo, Robert Lazarsfeld, Gregory G. Smith
By analyzing degeneracy loci over projectivized vector bundles, we recompute the degree of the discriminant locus of a vector bundle and provide a new proof of the Bogomolov instab…
Most secant varieties of tangential varieties to Veronese varieties are nondefective
Hirotachi Abo, Nick Vannieuwenhoven
We prove a conjecture stated by Catalisano, Geramita, and Gimigliano in 2002, which claims that the secant varieties of tangential varieties to the th Veronese embedding of the…
Eigenschemes and the Jordan canonical form
Hirotachi Abo, David Eklund, Thomas Kahle +1
We study the eigenscheme of a matrix which encodes information about the eigenvectors and generalized eigenvectors of a square matrix. The two main results in this paper are this d…