13 citations · 46 across the 18 of their papers we have counts for
16 papers · 1 filter
Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism
Valery Alexeev, Anand Deopurkar, Changho Han
We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable pairs -- compactifications of some moduli spaces of K3 surfaces with a nonsymplectic automorphism of order…
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…
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…
Anticanonical tropical cubic del Pezzos contain exactly 27 lines
Maria Angelica Cueto, Anand Deopurkar
The classical statement of Cayley-Salmon that there are 27 lines on every smooth cubic surface in P^3 fails to hold under tropicalization: a tropical cubic surface in TP^3 often co…
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…
Stable log surfaces, admissible covers, and canonical curves of genus 4
Anand Deopurkar, Changho Han
We explicitly describe the KSBA/Hacking compactification of a moduli space of log surfaces of Picard rank 2. The space parametrizes log pairs where is a degeneration o…
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…
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…
Green's canonical syzygy conjecture for ribbons
Anand Deopurkar
Green's canonical syzygy conjecture asserts a simple relationship between the Clifford index of a smooth projective curve and the shape of the minimal free resolution of its homoge…
Covers of stacky curves and limits of plane quintics
Anand Deopurkar
We construct a well-behaved compactification of finite covers of a stacky curve using admissible cover degenerations. Using our construction, we compactify the space of tetragonal…
Toward GIT stability of syzygies of canonical curves
Anand Deopurkar, Maksym Fedorchuk, David Swinarski
We introduce the problem of GIT stability for syzygy points of canonical curves with a view toward a GIT construction of the canonical model of the moduli space of stable curves. A…
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…
Sharp slope bounds for sweeping families of trigonal curves
Anand Deopurkar, Anand Patel
We establish sharp bounds for the slopes of curves in that sweep the locus of trigonal curves, proving Stankova-Frenkel's conjectured bound of for even and…
Compactifications of Hurwitz spaces
Anand Deopurkar
We construct several modular compactifications of the Hurwitz space of genus curves expressed as -sheeted, simply branched covers of genus curves. These comp…
Modular compactifications of the space of marked trigonal curves
Anand Deopurkar
We construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent. Beginning with the standard…