13 citations · 41 across the 21 of their papers we have counts for
25 papers
The Simplicity of the Hodge Bundle
Anand Patel
This paper shows that the Hodge bundle over the moduli space of genus curves does not contain any non-trivial sub-bundles. Notably, the mathematical content was generate…
Counting sums of two powers
Anand Patel
We generalize two well-known enumerative facts. The first, due to Clebsch, says that a general binary sextic form is expressible as the sum of a cube and a square in 40 different w…
Counting 3-uple Veronese surfaces
Anand Deopurkar, Anand Patel
This paper culminates in the count of the number of 3-Veronese surfaces passing through 13 general points. This follows the case of 2-Veronese surfaces discovered by Coble in the 1…
Complete Families of Generic Covers of Elliptic Curves
Gabriel Bujokas, Anand Patel
We introduce and motivate a conjecture about the existence of complete, 1-dimensional families of covers of an elliptic curve. If the conjecture holds, then it would imply a unifor…
Orbits of linear series on the projective line
Anand Deopurkar, Anand Patel
We compute the equivariant fundamental class of the orbit closure of a linear series on the projective line. We also describe the boundary of the orbit closure and how the orbits s…
Lines highly tangent to a hypersurface
Anand Patel, Eric Riedl, Geoffrey Smith +1
We study spaces of lines that meet a smooth hypersurface X in P^n to high order. As an application, we give a polynomial upper bound on the number of planes contained in a smooth d…
Bounding Pinch Point Schemes of Projected Surfaces
Adam Cartisano, Anand Patel
Let be a smooth surface and let , with , be a finitely ramified map which is birational onto its image , with non-degenerate in $\mat…
A Universal Formula For Counting Cubic Surfaces
Anand Deopurkar, Anand Patel, Dennis Tseng
Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit…
Moduli of linear slices of high degree hypersurfaces
Anand Patel, Eric Riedl, Dennis Tseng
We study the variation of linear sections of hypersurfaces in . We completely classify all plane curves, necessarily singular, whose line sections do not vary maximal…
Equivariant Degenerations of Plane Curve Orbits
Mitchell Lee, Anand Patel, Dennis Tseng
In a series of papers, Aluffi and Faber computed the degree of the orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by stu…
Ramification divisors of general projections
Anand Deopurkar, Eduard Duryev, Anand Patel
We study the ramification divisors of projections of a smooth projective variety onto a linear subspace of the same dimension. We prove that the ramification divisors vary in a max…
The rank two -curvature conjecture on generic curves
Anand Patel, Ananth N. Shankar, Junho Peter Whang
We prove the -curvature conjecture for rank two vector bundles with connection on generic curves, by combining deformation techniques for families of varieties and topological a…
Syzygy divisors on Hurwitz spaces
Anand Deopurkar, Anand Patel
We describe a sequence of effective divisors on the Hurwitz space for dividing and compute their cycle classes on a partial compactification. These divisors ari…
Orbits in and equivariant quantum cohomology
Mitchell Lee, Anand Patel, Hunter Spink +1
We compute the -equivariant Chow class of the -orbit closure of any point in terms of the rank polytope of the matroid…
Inflectionary Invariants for Isolated Complete Intersection Curve Singularities
Anand Patel, Ashvin Swaminathan
We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring singular members. Let , and consider an…
Vector bundles and finite covers
Anand Deopurkar, Anand Patel
Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz…
Moduli of Linear Sections of a General Hypersurface
Anand Patel
We investigate the global variation of moduli of linear sections of a general hypersurface. We prove a "generic Torelli" result for a large proportion of cases, and we obtain a com…
Interpolation in Algebraic Geometry
Aaron Landesman, Anand Patel
This is an expanded version of the two papers "Interpolation of Varieties of Minimal Degree" and "Interpolation Problems: Del Pezzo Surfaces." It is well known that one can find a…
Interpolation Problems: Del Pezzo Surfaces
Aaron Landesman, Anand Patel
We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.
Special codimension one loci in Hurwitz spaces
Anand Patel
We investigate two families of divisors which we expect to play a distinguished role in the global geometry of Hurwitz space. In particular, we show that they are extremal and rigi…
On the Chow ring of the Hurwitz space of degree three covers of
Anand Patel, Ravi Vakil
We determine that the Chow ring (with -coefficients) of the Hurwitz space parametrizing degree three covers of is tautological. We also compute the rational…
Invariants of a general branched cover of
Gabriel Bujokas, Anand Patel
We investigate the resolution of a general branched cover in its relative canonical embedding . We conjecture that the syzygy bundles appe…
Extremal effective divisors of Brill-Noether and Gieseker-Petri type in
Dawei Chen, Anand Patel
We show that certain divisors of Brill-Noether and Gieseker-Petri type span extremal rays of the effective cone in the moduli space of stable genus one curves with ordered mark…
The Picard rank conjecture for the Hurwitz spaces of degree up to five
Anand Deopurkar, Anand Patel
We prove that the rational Picard group of the simple Hurwitz space is trivial for up to five. We also relate the rational Picard groups of the Hurwitz spa…