On the classification of irregular surfaces of general type with nonbirational bicanonical map期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

On the classification of irregular surfaces of general type with nonbirational bicanonical map

Authors:	Fabrizio Catanese Ciro Ciliberto Margarida Mendes Lopes

Institution:	Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy ; Dipartimento di Matematica, Università di Tor Vergata, Viale della Ric. Scientifica, 16132 Roma, Italy ; Dipartimento di Matemática, Faculdade de Ciencias de Lisboa, R. Ernesto de Vasconcelos, 1700 Lisboa, Portugal

Abstract:	The present paper is devoted to the classification of irregular surfaces of general type with $p_{g}\geq 3$ and nonbirational bicanonical map. Our main result is that, if is such a surface and if is minimal with no pencil of curves of genus , then is the symmetric product of a curve of genus , and therefore $p_{g}=q=3$ and $K^{2}=6$ . Furthermore we obtain some results towards the classification of minimal surfaces with $p_{g}=q=3$ . Such surfaces have $6\leq K^{2}\leq 9$ , and we show that $K^{2}=6$ if and only if is the symmetric product of a curve of genus . We also classify the minimal surfaces with $p_{g}=q=3$ with a pencil of curves of genus , proving in particular that for those one has $K^{2}=8$ .

Keywords:

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文