E. Schlesinger

activity

19992025

most citedHilbert Schemes of Degree Four Curves

2 citations · 4 across the 12 of their papers we have counts for

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13 papers · 1 filter

math.AG2025

Multiple Lines of Maximum Genus in $P^{3}$

Enrico Schlesinger

We introduce a notion of good cohomology for multiple lines in $P^{3}$ and we classify multiple lines with good cohomology up to multiplicity 4. In particular, we show that…

math.AG2021

Reconstructing curves from their Hodge classes

Maria Gioia Cifani, Gian Pietro Pirola, Enrico Schlesinger

Let $S$ be a smooth algebraic surface in $P^{3} (C)$ . A curve $C$ in $S$ has a cohomology class $η_{C} \in H^{1} (Ω_{S}^{1})$ . Define $α (C)$ to be…

math.AG2018

The maximum genus problem for locally Cohen-Macaulay space curves

Valentina Beorchia, Paolo Lella, Enrico Schlesinger

Let $P_{MAX} (d, s)$ denote the maximum arithmetic genus of a locally Cohen-Macaulay curve of degree $d$ in $P^{3}$ that is not contained in a surface of degree $< s$ . A…

math.AG2012

Smooth curves specialize to extremal curves

Robin Hartshorne, Paolo Lella, Enrico Schlesinger

Let $H_{d, g}$ denote the Hilbert scheme of locally Cohen-Macaulay curves of degree $d$ and genus $g$ in projective three space. We show that, given a smooth irreducible curve $C$ o…

math.AG2011

The Hilbert schemes of locally Cohen-Macaulay curves in P^3 may after all be connected

Paolo Lella, Enrico Schlesinger

Progress on the problem whether the Hilbert schemes of locally Cohen-Macaulay curves in projective 3 space are connected has been hampered by the lack of an answer to a question th…

math.AG2010

A New Curve Algebraically but not Rationally Uniformized by Radicals

Gian Pietro Pirola, Cecilia Rizzi, Enrico Schlesinger

We give a new example of a curve C algebraically, but not rationally, uniformized by radicals. This means that C has no map onto the projective line P^1 with solvable Galois group,…

math.AG2008

Gonality of a general ACM curve in projective 3-space

Robin Hartshorne, Enrico Schlesinger

Let C be an ACM (projectively normal) nondegenerate smooth curve in projective 3-space, and suppose C is general in its Hilbert scheme - this is irreducible once the postulation is…

math.AG2006

Codimension 3 Arithmetically Gorenstein Subschemes of projective $N$ -space

R. Hartshorne, I. Sabadini, E. Schlesinger

We study the lowest dimensional open case of the question whether every arithmetically Cohen--Macaulay subscheme of $P^{N}$ is glicci, that is, whether every zero-scheme in…

math.AG2004

A curve algebraically but not rationally uniformized by radicals

Gian Pietro Pirola, Enrico Schlesinger

Zariski proved the general complex projective curve of genus g>6 is not rationally uniformized by radicals, that is, admits no map to the projective line whose Galois group is solv…

math.AG2004

Monodromy of Projective Curves

Gian Pietro Pirola, Enrico Schlesinger

The uniform position principle states that, given an irreducible nondegenerate curve C in the projective r-space $P^{r}$ , a general (r-2)-plane L is uniform, that is, projection from…

math.AG2001★ 2 cited

Curves on a Double Surface

Scott Nollet, Enrico Schlesinger

Let F be a smooth surface in a smooth projective threefold T, and let X=2F be the first infinitesimal neighborhood of X in T. A locally Cohen-Macaulay curve C in X gives rise to tw…