Rational cuspidal curves on del-Pezzo surfaces

DOI10.5427/jsing.2018.17fzbMath1423.14308arXiv1509.06300OpenAlexW2964222969WikidataQ129889548 ScholiaQ129889548MaRDI QIDQ4638257

Indranil Biswas, Ritwik Mukherjee, Shane D'Mello, Vamsi Pritham Pingali

Publication date: 4 May 2018

Published in: Journal of Singularities (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.06300

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Families, moduli of curves (algebraic) (14H10) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Fano varieties (14J45)

Related Items

Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure, Counting rational curves with an \(m\)-fold point, Rational cuspidal curves in a moving family of \(\mathbb{P}^2\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Enumeration of curves with one singular point
• A proof of the Göttsche-Yau-Zaslow formula
• Enumeration of curves with two singular points
• Universal polynomials for tautological integrals on Hilbert schemes
• A short proof of the Göttsche conjecture
• The quantum cohomology of blow-ups of \(\mathbb{P}^2\) and enumerative geometry
• Genus two enumerative invariants in del-Pezzo surfaces with a fixed complex structure
• Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure
• Enumeration of genus-two curves with a fixed complex structure in \(\mathbb{P}^2\) and \(\mathbb{P}^3\)
• Genus \(1\) enumerative invariants in \(\mathbb{P}^n\) with fixed \(j\) invariant
• Tautological integrals on curvilinear Hilbert schemes
• Enumeration of singular algebraic curves
• Universal polynomials for singular curves on surfaces
• On the Enumeration of Complex Plane Curves with Two Singular Points
• The irreducibility of the spaces of rational curves on del Pezzo surfaces
• Geometry of the Severi Variety
• Counting Divisors with Prescribed Singularities
• Intersections of ℚ-divisors on Kontsevich’s moduli space \overline{𝕄}_{0,𝕟}(ℙ^{𝕣},𝕕) and enumerative geometry
• Bend, break and count II: elliptics, cuspidals, linear genera
• Counting elliptic plane curves with fixed $j$-invariant
• Characteristic numbers of rational curves with cusp or prescribed triple contact
• Enumeration of genus-three plane curves with a fixed complex structure
• Node polynomials for families: methods and applications
• Multisingularities, cobordisms, and enumerative geometry
• Enumeration of $n$-fold tangent hyperplanes to a surface
• Curve Counting \`a la G\"ottsche
• A mathematical theory of quantum cohomology