9 citations · 50 across the 13 of their papers we have counts for
13 papers
Degenerations of Grassmannians via lattice configurations II
Xiang He, Naizhen Zhang
This paper is a continuation of our study of degenerations of Grassmannians in our last paper, called linked Grassmannians, constructed using convex lattice configurations in Bruha…
Weierstrass semigroups from cyclic covers of hyperelliptic curves
Ethan Cotterill, Nathan Pflueger, Naizhen Zhang
The {\it Weierstrass semigroup} of pole orders of meromorphic functions in a point of a smooth algebraic curve is a classical object of study; a celebrated problem of Hurwi…
Hyperkähler geometry of rational curves in twistor spaces
Roger Bielawski, Naizhen Zhang
We investigate the pseudo-hyperkähler geometry of higher degree rational curves in the twistor space of a hyperkähler -manifold.
When are multidegrees positive?
Federico Castillo, Yairon Cid-Ruiz, Binglin Li +2
Let be an arbitrary field, be a multiprojective space over , and be a closed subscheme of . We provide…
Degenerations of Grassmannians via lattice configurations
Xiang He, Naizhen Zhang
We study degenerations of Grassmannians constructed using convex lattice configurations in Bruhat-Tits buildings. Using techniques from quiver representations, we analyze their spe…
The Strong Maximal Rank Conjecture and higher rank Brill--Noether theory
Ethan Cotterill, Adrián Alonso Gonzalo, Naizhen Zhang
In this paper, we compute the cohomology class of certain "special maximal-rank loci" originally defined by Aprodu and Farkas. By showing that such classes are nonzero, we are able…
Secant planes of a general curve via degenerations
Ethan Cotterill, Xiang He, Naizhen Zhang
We study linear series on a general curve of genus g, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded…
The strong maximal rank conjecture and moduli spaces of curves
Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas +1
Building on recent work of the authors, we use degenerations to chains of elliptic curves to prove two cases of the Aprodu-Farkas strong maximal rank conjecture, in genus and…
Limit linear series and ranks of multiplication maps
Fu Liu, Brian Osserman, Montserrat Teixidor I Bigas +1
We develop a new technique for studying ranks of multiplication maps for linear series via limit linear series and degenerations to chains of genus-1 curves. We use this approach t…
Representable Chow classes of a product of projective spaces
Federico Castillo, Binglin Li, Naizhen Zhang
Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroi…
Towards the Bertram-Feinberg-Mukai Conjecture
Naizhen Zhang
In this paper, we prove the existence portion of the Bertram-Feinberg-Mukai Conjecture for an infinite family of new cases using degeneration technique. This not only leads to a su…
Expected Dimensions of Higher-rank Brill-Noether Loci
Naizhen Zhang
In this paper, we prove a new expected dimension formula for certain rank two Brill-Noether loci with fixed special determinant. This answers a question asked by Osserman and also…
Polynomial recursion formula for linear Hodge integrals
Motohico Mulase, Naizhen Zhang
We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show…