3 citations · 4 across the 7 of their papers we have counts for
13 papers · 1 filter
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…
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…