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Damiano Testa

Publications and source records attributed to Damiano Testa.

26 records · Page 2Linked to original sources
arXiv2013

Plane quartics with at least 8 hyperinflection points

A recent result shows that a general smooth plane quartic can be recovered from its 24 inflection lines and a single inflection point. Nevertheless, the question whether or not a smooth plane curve of degree at least 4 is determined by its inflection lines is still open. Over a field of characteristic 0, we show that it is possible to reconstruct any smooth plane quartic with at least 8 hyperinflection points by its inflection lines. Our methods apply also in positive characteristic, where we show a similar result, with two exceptions in characteristic 13.

math.AG↗
arXiv2011

Recovering plane curves of low degree from their inflection lines and inflection points

In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree at least three from its inflection lines? We answer positively to the posed question for a general smooth plane quartic curve, making the additional assumption that also one inflection point is given, and for any smooth plane cubic curve.

math.AG↗
arXiv2009

Cox rings of degree one del Pezzo surfaces

Let X be a del Pezzo surface of degree one over an algebraically closed field (of any characteristic), and let Cox(X) be its total coordinate ring. We prove the missing case of a conjecture of Batyrev and Popov, which states that Cox(X) is a quadratic algebra. We use a complex of vector spaces whose homology determines part of the structure of the minimal free Pic(X)-graded resolution of Cox(X) over a polynomial ring. We show that sufficiently many Betti numbers of this minimal free resolution vanish to establish the conjecture.

math.AG↗
arXiv2009

Big rational surfaces

We prove that the Cox ring of a smooth rational surface with big anticanonical class is finitely generated. We classify surfaces of this type that are blow-ups of the plane at distinct points lying on a (possibly reducible) cubic.

math.AG↗
arXiv2007

Cores of simplicial complexes

We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. We give some applications of this method to complexes arising from graphs. As a consequence, we answer some questions raised in [R.Ehrenborg, G.Hetyei, European J.Combin.27 (2006), no.6, 906-923] on the independence complex and the dominance complex. The techniques used come mainly from monomial ideal theory.

math.CO↗
arXiv2006

Groebner bases, monomial group actions, and the Cox rings of Del Pezzo surfaces

We introduce the notion of monomial group action and study some of its consequences for Groebner basis theory. As an application we prove a conjecture of V. Batyrev and O. Popov describing the Cox rings of Del Pezzo surfaces (of degree at least 3) as quotients of a polynomial ring by an ideal generated by quadrics.

math.AC↗